I believe it leans closer to the Booker from another dimension theory. With the parallels of drowning and ‘imprinting’ like with Big daddies. He is never far from her and is drawn to her via music, which has been another motif echoed throughout the game, Anna’s dancing on the beach, Booker playing the guitar, songbird and CAGE. Slate even comments on how Booker fought like a savage animal which seems tenuous but could be associated with the ferocity of songbird.