Reposting a post from another thread on the story and ending for discussion:
[spoiler]
As far as I can figure it, this is how everything goes down:
Booker returns from the war. We have the universe/timeline split at the Baptism.
Our Booker (we'll call him Booker A), rejects the Baptism, becomes a cynical bastard, gambles, and ends up with a huge amount of debt. Then we put universe A on hold for a bit.
Meanwhile, in Universe B, Booker accepts the Baptism, becomes Comstock, and builds Columbia with the Lutece girl. She manages to find her twin in Booker A's reality, and gets him to buy Elizabeth and bring her to their reality. Booker tries to stop it, but he can't, which is how Elizabeth ends up with a severed finger.
Comstock (or Booker B), being the crazy bastard that he is, kills his wife and the Lutece twins to keep his secret. The twins, however, know all this shit anyway because they understand how everything works, feel bad about what they did, and go back and try to fix it by bringing Booker A in at the beginning of the game.
Now here's where it gets complicated.
This has happened an infinite amount of times. Every choice each Booker makes creates a new universe, giving him a new chance to put things right. Remember when the twins would make you make all those random choices? That's why. Each choices spins off a parallel universe. No matter how many times they do this, though, Booker always, always gets stopped by the Songbird before he can get to Elizabeth, which results in some variation of future Elizabeth burning down New York.
However, this time, Booker manages to get to future Elizabeth, who seems him back just in time to prevent her from being brainwashed. They destroy the Siphon, and Elizabeth basically becomes a god.
The problem is, they still have to stop Comstock. Every Comstock. At the same time. Because doing it individually would results in more universes being created because something would inevitably change [ie, the coin flip (which is always, always heads, but if you call tails, boom, another universe) or the pendant choice, killing or sparing Slate, etc] which also creates more realities. And besides, one of the constants in all the universes is that Booker always fails (except in the one Booker A occupies in the game where he succeeds due to Old Lady Elizabeth).
So to stop everything, they have to go back to the original reality where Booker A (our Booker) chooses to accept the Baptism. They then drown him, preventing any Booker from ever becoming Comstock. Since he died at that moment, all of those universes are never created, and so cease to exist, which is shown when all but one of the Elizabeths disappear (she corresponds to the revised timeline).
So Anna is never sold off, Booker never becomes Comstock, Columbia is never created, the Lutece's never play with quantum mechanics, the deal is never made and none of it ever happens.
Which leaves us with Booker A, who rejects the baptism, in his room, going to check on his daughter, who, if all else holds true, should still be there.
Elizabeth, as we know her, however, ceases to exist.
[/spoiler]
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