COMMUTER HAS CLOSE PROX WITH ACR ACFT RESPONDING TO TCASII.

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WHILE ACTING AS PIC FOR COMMUTER FLT WE DEPARTED BOSTON CLBING TO 4000 FT. WE WERE ASSIGNED A HDG OF 360 DEGS FOR TFC WHICH WAS IN OUR 12-2 O'CLOCK POS AT 4700 FT. WITH TFC IN SIGHT; WE WERE CLRED TO CLB TO 12000 FT WHILE MAINTAINING VISUAL SEPARATION. ALSO; A DIRECT PEASE WHEN ABLE WAS RECEIVED. AN ACR Y FLT WAS ADVISED THAT WE WOULD BE APCHING FROM THEIR 6 O'CLOCK POS AND WOULD BE OVERTAKING THEM WHILE MAINTAINING VISUAL SEPARATION. SHORTLY AFTER THAT; ACR Y ASKED THE CTLRS IF THEY SHOWED TFC NEAR THEM. ONCE AGAIN THE CTLR ADVISED THEM OF US. WE KEPT THEM ON OUR L SIDE; PASSED ON THEIR R AT A SAFE DISTANCE. ACR Y CHANGED THEIR COURSE TO THE L AND DSNDED. SINCE WE WERE STILL BELOW THEM AT THE TIME (AND CLBING); THEIR DSCNT DID BRING US A LITTLE CLOSER; BUT AT NO TIME WAS SAFETY COMPROMISED. ACR Y RPTED THAT THEIR TCASII ADVISED THEM OF TFC. I DID TELL THE ACR Y CREW THEY SHOULD GET THEIR EQUIP CHKED. IF INDEED THEIR TCASII TOLD THEM TO DSND AND TURN L; ONE WOULD HAVE TO QUESTION THE RELIABILITY OF THE TCASII EQUIP IN A REAL COLLISION AVOIDANCE SIT. OUR ACFT WAS NOT EQUIPPED WITH TCASII.