DC-9 ACFT IN CLB WAS STOPPED SHORT OF ASSIGNED ALT DUE TO HIGHER TFC. ALT ALERTER NOT RESET AND PF; THOUGHT THEY WERE STILL GOING TO THE ORIGINAL ALT AND COMMENCED CLB CAUSING LOSS OF SEPARATION AND TCASII ALERTS ON BOTH ACFT.

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I WAS ACTING AS PIC OF A SCHEDULED PART 121 FLT FROM NEW YORK (LGA) TO COLUMBUS; OHIO (CMH). WE WERE BEING VECTORED BY NEW YORK CTR AND FLYING AN ASSIGNED HDG PARALLEL TO OUR ROUTE; J-80. WE RECEIVED A CLRNC TO CLB TO FL280. WE SET THE ALT ALERTER AND STARTED OUT FROM FL230. SHORTLY AFTER PASSING FL250 (ABOUT 25200 FT) CTR INSTRUCTED US TO LEVEL AT FL260. THE ACFT WAS BEING FLOWN BY THE FO AND WAS CLBING AT A RAPID RATE; SO HE HURRIEDLY LEVELED AT FL260. AT THE SAME TIME CTR ADVISED US OF TFC AT OUR 10 O'CLOCK POS; AND AT FL270. I WAS LOOKING FOR THE TFC AND HAD HIM IN SIGHT. OUR FLT PATHS WERE MERGING. WHILE I WAS WATCHING THE ACFT MY ATTN WAS DRAWN BACK INSIDE TO THE IVSI WHICH HAD ILLUMINATED AND OUR TCASII ALERT WENT OFF. I IMMEDIATELY SAW THAT WE HAD DEPARTED FL260 AND WERE CLBING. WE HAD ALREADY PASSED FL265 WHEN I INSTRUCTED THE FO TO RETURN TO FL260 ASAP!! WE DID SO BUT NOT BEFORE SETTING OFF AN RA FOR THE OTHER ACFT WHO STARTED TO CLB. CTR ASKED US OUR ALT AND BY THEN WE WERE JUST ABOUT LEVEL AT FL260 AGAIN. THE ERROR IN THIS SIT WAS OURS. ALTHOUGH WE WERE LEVELED AT FL260 WE NEVER HAD A CHANCE TO RESET OUR ALT ALERTER AND AFTER A FEW MINUTES THE FO THOUGHT WE HAD BEEN RE-CLRED TO FL280; BUT WE HAD NOT BEEN DUE TO THE FLT ABOVE US AT FL270 AND MERGING FROM OUR L. I FAILED TO CATCH THE CLB BECAUSE I WAS KEEPING THE ACFT IN SIGHT. I DO FEEL THAT CONTRIBUTING FACTORS ARE THE AMOUNT OF RADIO CALLS AND FREQUENCY CHANGES REQUIRED WHEN DEPARTING NEW YORK. FREQUENTLY THERE ARE NUMEROUS CALLS REQUIRED TO CONTACT NEW YORK CTR CTLRS. THERE IS A HIGH AMOUNT OF VECTORING AND ALT CLRNCS ISSUED. THESE EVENTS HAPPEN AT A RAPID PACE. SOMETIMES IT BECOMES DIFFICULT TO KEEP UP.