B757-200 FLT CREW PROGRAMMED AND INITIALLY FLEW THE WRONG TRANSITION FOR THE PUBLISHED SID.

Narrative

ON DEP OUT OF JFK ON KENNEDY ONE BREEZY POINT CLB PASSING CRI; THE FO STARTED TO TRACK THE CANARSIE CLB (176 DEG RADIAL OUT OF CRI) INSTEAD OF THE 223 DEG RADIAL ON THE BREEZY POINT CLB. ATC AND MYSELF RECOGNIZED THE TURN AT ABOUT THE SAME TIME AND ATC ISSUED A TURN BACK TO 240 DEGS TO CORRECT BACK TO COURSE. I ALSO MANUALLY TURNED THE VOR TO CRI 223 DEG RADIAL AND CONFIRMED THE CORRECTION BACK TO COURSE. THE FLT THEN PROCEEDED AS CLRED BACK ON THE DEP AND TO DEST. FO WAS HAND FLYING IN LNAV WITH FLT DIRECTOR ON. WE HAD FLOWN AN ALL-NIGHTER INTO JFK THAT MORNING WITH A FIELD LAYOVER AND DEP BACK TO ZZZ THAT EVENING. A FACTOR OF CONCERN IS THAT THE KENNEDY ONE DEP HAS A SELECTABLE CRI TRANSITION AND THE RWY 31L DEP FLIES OVER CRI EVEN ON THE BREEZY POINT CLB. THE CANARSIE TRANSITION SHOULD BE SPELLED OUT DIFFERENTLY IN THE FMS DATABASE TO MAKE THIS DIFFERENCE STAND OUT AND AVOID CONFUSION. SUPPLEMENTAL INFO FROM ACN 742769: I SUGGEST MAYBE THE FMC SHOULD HAVE THE SELECTION OF THE CANARSIE TRANSITION CHANGED TO READ CANARSIE VICE CRI.