B737-300 FLT CREW IS ISSUED MULTIPLE ALT CHANGES BY N90 APCH APPARENTLY DUE TO UNTIMELY AIRSPACE COORD CONFIGN CHANGES.

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DEPARTING CAMRN; ATC CLRNC WAS HEADING 040 DEGS; 6000 FT MSL. UPON REACHING 6000 FT; ATC IMMEDIATELY CALLED FOR US TO CLB TO 7000 FT. AS WE REESTABLISHED OUR CLB PASSING 6200 FT; ATC RECLRED US TO 6000 FT; THEN 5000 FT. NO EXPLANATION FOR THE VARIANCE IN ALTS. BOTH CAPT AND I RECONFIRMED THAT WE BOTH HAD ORIGINALLY HEARD AND ACKNOWLEDGED TO ATC 6000 FT; THUS THE VERY APPREHENSION THAT WE BUSTED ALT ASSIGNMENT. I CALLED TRACON UPON LNDG AND THEY CONFIRMED THAT WE WERE ASSIGNED 6000 FT; NOT 7000 FT ORIGINALLY. BOTH THE CTLR AND SUPVR ON DUTY ADMITTED THAT IT WAS ATC ERROR; IN THAT THERE ARE NEW AIRSPACE PROCS IN PLACE FOR THAT PARTICULAR AIRSPACE; TIME OF DAY; AND WHEN ILS RWY 22L JFK IS IN USE AND THAT THEY WERE ACTUALLY IN A TURNOVER OR SWITCHOVER (ASSIGNING 6000 FT OR 7000 FT) TIME FRAME WHEN THEY PICKED UP OUR FLT. BOY; WHAT A WINDOW TO BE IN AT THE WRONG TIME AND WRONG PLACE. ALL WAS RESOLVED AND ALL HAPPY. NO ATC CONFLICT; BUT WE DID GET A TCASII ALERT WITH TFC RIGHT BELOW US AT 5000 FT.