Elizabeth "killed" him, but Elizabeth also has the power to alter space and time, and it's not like you see any body in the pull-out shot of the baptizing area
the very last shot (after the credits, in the office) could be from any number of possibilities, since there's nothing else there besides Booker saying anna's name and opening the room door (you never get to see Anna before the shot cuts), it could be ANYTHING.
the whole point in killing Booker at that point is that in some tears he baptizes himself and changes his name to Comstock as a man "born again", in some tears he does NOT go ahead with that choice.
the entire plot exists because of "a lady" because she's the one who is the first person to make the breakthrough of the quantum mechanics and discovers alternate realities, in one of the realities she's "a gentleman" which is why she calls him her brother, this was in one of the radios btw, so in one of the tears where booker baptized himself, he came upon "a lady" and with her help created the sky city, built himself as a prophet and then got full of himself to the point of believing himself as a prophet.
then he married lady comstock, but she couldn't conceive a child, so he uses "a lady" to build a portal, and rather then take anyone else's child, decides to take his own child from a timeline where he didn't baptize himself and ends up a failed private detective with a large debt.
again, "a lady" and "a gentlemen" are the primary people responsible for pulling this version of booker into a tear timeline where comstock exists to get a hold of liz, and utilize her powers so things can be "halted" before they even began.
and the only way to stop all this shit is for booker to die before he is "born again" as zachery, or doesn't take the baptism, i-e he needs to be killed BEFORE he goes ahead with that choice, and that's why all the elizibeth's are there to help kill him, once he dies, all the alternate elizibeth's on site disappear because their timelines don't exist anymore, except for the elizibeth who accompanied booker, because she's the elizibeth from the primary timeline where booker sold his daughter and went on this adventure to begin with, i-e she's from what you can call "the real timeline" at that point.