Significance of the nosebleeds?

If I remember right, the nosebleeds occur when Booker either dies in a different reality, or when he's remembering things that happened to him in a different reality.

"Greetings! This is not God, but his close friend, Officer Boscorelli. Please pull over."- Bosco

It's like the nose bleeds in that time travel movie, Butterfly Effect. (or some other movie, too many to recall, something to do with inscription error)

It does seem to honor the movie Butterfly Effect. In fact, *spoiler alert*, there is an alternate ending of Butterfly Effect where he chokes himself to death/misscarriage on the umbilical cord in the womb because the only way to save everyone elses lives and make them better is by ending himself. He is the one constant that ruins outcomes for all possible equations. Like if Damion from the Exorcist chose suicide over accepting he is Lucifer, destroyer of all that is good. Or, the opposite of "It's A Wonderful Life", where you are worth more dead, than alive, to entire realities. Pretty somber and grim if you ask me, but I always was a sarcastic Ecclesiastes kind of philosopher at heart.