A CESSNA 421, N247CB, WAS RECEIVING RADAR ADVISORIES FROM NEW YORK TRACON WHILE PROCEEDING WESTBOURND AT 10,500 FT. AT ABOUT THE SAME TIME, PAN AM FLT 542 (BOEING 727, N553PE) WAS PROCEEDING NORTHEAST AT 10,000 FT WITH AN IFR CLNC. AT 1744:32 EDT, THE LIBERTY SECTOR CTLR GAVE THE CESSNA PLT A FREQ CHANGE TO THE LAGUARDIA SECTOR, WHICH WAS THE NEXT SECTOR TO THE WEST; HE THEN CHANGED THE CESSNA 421'S DATA BLOCK TO A LIMITED DATA BLOCK. AT 1748, FLT 542 WAS GIVEN A FREQ CHANGE FROM THE LAGUARDIA SECTOR TO THE LIBERTY SECTOR. AT 1749:04, BEFORE THE TWO ACFT HAD PASSED EACH OTHER, THE LIBERTY SECTOR CTLR CLRD FLT 542 TO CLIMB TO 17,000 FT & TO TURN TO A HDG OF 080 DEG. THE CESSNA PLT HAD BEEN GIVEN A TRAFFIC ADVISORY (BY THE LAGUARDIA CTLR) & WAS WATCHING FLT 542. WHEN THE CESSNA PLT REALIZED FLT 542 HAD STARTED TO CLIMB, HE PULLED UP TO AVOID A COLLISION. AT ABOUT THE SAME TIME, ONE OF THE PLTS OF FLT 542 SAW THE CESSNA & PUSHED THE NOSE OF HIS ACFT DOWN FOR EVASIVE ACTION.