MD88 FLC MAINTAINING VISUAL SEPARATION CAUSES TCASII ALERT IN SEPARATION TFC ACFT.

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WE WERE LEVEL AT 16000 FT AFTER CLBING OUT OF BOSTON ON ZBW FREQ. AN ACR SAAB 340 TFC WAS CALLED OUT TO US AT 11 O'CLOCK POS AND 15 MI; XING L TO R. WE PICKED UP THE TFC AND HAD A VISUAL AT 10 MI. HE WAS LEVEL AT 17000 FT. WHEN WE CALLED VISUAL; CTR ASKED US TO MAINTAIN VISUAL SEPARATION AND CLRED TO CLB TO FL230. WE STARTED AN IMMEDIATE CLB MAINTAINING VISUAL SEPARATION. PASSING THROUGH 17000 FT; WE WERE CLBING AT 5000 FPM AND STILL HAD ADEQUATE VISUAL SEPARATION. AS WE CROSSED OVER HIM; HE WAS SLIGHTLY R OF THE NOSE AND APPROX 1300-1500 FT BELOW US. THE TCASII CALLED OUT THE TFC AND WE WERE VISUALLY WELL CLR. APPARENTLY HE WAS A LITTLE CONCERNED BECAUSE HE NEVER HAD A VISUAL ON US AND HIS TCASII WAS GIVING HIM A TA OR RA WARNING. HE ASKED CTR FOR OUR CALL SIGN. THE TCASII LAGGED BEHIND US A BIT BECAUSE OF OUR HIGH RATE OF CLB. IN THE FUTURE I WILL HESITATE TO TAKE VISUAL CLBS TAKING TCASII AND ITS WARNINGS INTO CONSIDERATION. WE BOTH SHOULD HAVE HAD A VISUAL OR; BETTER YET; I SHOULD HAVE HAD MAINTAINED 16000 FT UNTIL WELL CLR AND DECLINED THE VISUAL CLB.