So this is the way I see how the story played out. Its very dificult to think about time in a way thats easy for us to imagine. The best way I can conceptualize it in my head, at least as far as this fiction goes, is to think of time not as a single endless loop or a straight line, but as a infinite parallel math equation that are constantly looping, infinitely. This equation, as many often do, contains constants and variables represented via multiple parralel loops. Every time the equation is run, ad-infinium, the variables can change but the constants remain the same.

Now, that said, this is how I see the ending. We all know that the baptism is a constant; Elizabeth pretty much lays that out, and the variable is Booker's decision whether or not to be baptized. We know that if he does get baptized he changes his name to Comstock, creates columbia, discovers multiple dimensions (via Lutece), sees a future in which his daughter will rain fire upon the sodom below, finds out he's setril, finds out about Booker and that hes a deadbeat dad, Convinces him to sell Anna, Anna becomes Elizabeth (I believe at this point Elizabeth becomes a constant, will explain below),Then the story begins.

If Booker denies the baptism, he falls down a pit of alcoholism, debt, depression, and single fatherhood. He then sells his daughter to a man who claims he'll wipe away his debt (male Lutece) and in a failed attept to get her back accidentally causes her finger to be chopped off by a closing rift, allowing her to exist in multiple dimensions at once and therefore making her a constant, or a witch... He then continues his downward spiral of drunken self pity until one day a man shows up, once again male Lutece only this time with his own intentions in mind. He offers Dewitt the ability to redeem his sins, save his daughter, and as a result prevent the armageddon made possible by Lutece's brilliance. Lutece, then brings Booker into the Comstock reality (think of them as paralell instances of the same equation being run with different variables) and again, the story begins.

Fast forward to the end, Elizabeth's shackles are removed and shes now the coolest thing since Neo. From the hints given in various locations, I think its safe to say that the reason she has these powers is because she physically exists in two seperate universes at the same time (via pinky incident). My personal theory on this, again thinking of the universe as this logical, mathematical computer, I would think there have to be failsafes in check, things to prevent itself from failure due to things like paradoxes. That said, what I like to think is happening is that Elizabeth has more or less ben "given" this power as a form of "elevated privaleges" so that she would have the necessary access to resolve/prevent a paradox, which she then uses to create one.

Now for the part the gets tough, Elizabeth and Booker take a stroll through the multiverse and then the big reveal happens, Booker is Comstock and the only way to prevent all this crazy shit from happening in every dimension is to create a new constant that will prevent Booker from ever becoming Comstock, they need to kill Booker before he accepts the Baptism. From there, Elizabeth brings Booker to a new door, which leads to a lake at what I think is safe to assume is sometime shortly before he gets baptised. We then watch as Elizabeths from multiple realities appear. In my opinion this is a visualization of Elizabeth turning this moment into a constant, Elizabeth has the ability to see and, as it seems in some way control alternate versions of herself throught multiple realities, making it possible for her to "create" constants at the same point in every common parallel equation. But one thing I think is important to recognize that this constant's very existence directly relies on the existence of Eliazbeth, more on that later.

As we slowly watch Booker drown from a first person perspective, we see all the different Elizabeth's dissapear one by. As Booker dies, we get one last shot our Elizabeth, then black. Im again going to use the Equation metaphor here as I image each of these Elizabeth's timelines collapsing on themselves as their loops are broken by the paradox, with the final universal collapse being ours, cut to black.

Now, just in case this wasnt all a bit subjective to begin with, then we get the post credit bombshell that sent everyone to GameFAQS in utter confusion. Well heres one mans huble attempt to explain the biggest question of Bioshock Infinite, HOW THE FUCK IS BOOKER ALIVE? To answer this I'm going to refer back to two things, the first being to imagine these Infinite universes as parallel mathematical equations, looping infinitaley and sharing constants while having differing variables. The second is to remember how I mentioned that the final Constant created by Elizabeth which breaks the cycle is one thats very existence relies on the existence of Elizabeth. That said, what Elizabeth effectively did was remove the possibility of her own existence from the universe, because now in any possibility in which Elzabeth exists will now result in a paradox and has been made impossible. So if you again think about these looping equations, after the loop completes in which Elizabeth eisted and as a result destroys her own universe via the drowning of Booker it is now impossible for a tinmeline to exist in which Elizabeth exists, if Elizabeth cant exist, then Comstock definitely can't exist, and also if Elizabeth doesnt exist, she cant loop around her own timeline and drown Booker. This leaves Booker back at the Baptism, the first loop since the collapse. So now your totally like, "BUT WAIT, THAT MEANS WE DIDNT SOLVE ANYTHING, IF HES BACK AT THE BAPTISM HE CAN CHOOSE TO BECOME COMSTOCK AGAIN!?!?!?!!!!"

Well, not exactly, lets take a look back at that equation, if Booker becomes Comstock, Elizabeth happens. If Elizabeth happens, Booker will travel to columbia and save her, If that happens, Elizabeth will take Booker back in time and kill himself before the baptism, again creating another paradox and collapsing the timeline. Its all self-fulfilling. By creating the causality loop/paradox, Elizabeth has made Bookers decision to accept Baptism and become Comstock a universal impossibility, leaving him with only one choice, to reject his baptism, and live his life with Anna. Without the possibility of Comstock, this Anna will never be kidnapped, turned into the Scarlet Witch, and used as a WMD.

I hope that all makes sense, or its just a pile of nonesense, either way.

I believe your notion of "infinite loops" is what's confusing.

In the end, nothing you did in the game happened. The game was made possible because of Comstock. Without him, there is no Elizabeth, Lutece, Columbia, etc. At the end of the game you're just a former Pinkerton agent with a daughter named Anna.