TCASII AND APCH CTLRS COMBINE TO EVADE TFC.

Narrative

PIT APCH INSTRUCTED OUR ACFT TO DEPART CUTLA INTXN ON A 180 DEG HDG; FOLLOWED BY A CLRNC TO SLOW TO 210 KIAS; THEN DSND AND MAINTAIN 6000 FT. AFTER SLOWING TO 210 KTS AND DURING THE DSCNT FROM 10000 FT TO 6000 FT; WE WERE IN VISUAL CONTACT AND TCASII CONTACT WITH 6000 FT TFC CONVERGING FROM OUR R 1-2 O'CLOCK. APCH CTL THEN GAVE US A TURN TO 230 DEGS; WHICH WOULD HAVE PUT US IN VERY CLOSE PROX TO OUR TFC. WE MOMENTARILY STOPPED OUR DSCNT AT 6500 FT AND QUERIED APCH CTL ABOUT OUR TFC. THE RESPONSE FROM PIT APCH INDICATED THEY NOW ALSO; RECOGNIZED THE CONFLICT. BECAUSE IT WAS VMC AND WE HAD A 'TALLY-HO' AS WELL AS TCASII CONTACT; WE WERE ABLE TO AVOID A NEAR MISS. AFTER THE FLT; WHEN SPEAKING TO THE CAPT ON THE TELEPHONE; PIT APCH THOUGHT THEY HAD CLRED US TO 7000 FT. BOTH THE CAPT AND I ACKNOWLEDGED 6000 FT. IT SOUNDED AS IF A SECOND VOICE (CTLR'S) CAME ON THE AIR AS THE SIT INFLT HAD PUT 2 ACFT IN SUCH CLOSE PROX. I SUSPECT THE CTLR MADE AN ERROR IN ASSIGNING US 6000 FT AND RECOGNIZED IT LATE. JUST AS WE CONFIRM OUR ALT ASSIGNMENTS; ATC MUST CONFIRM THE READBACK. SUPPLEMENTAL INFO FROM ACN 256927: ATC CTLR TRAINING WAS IN PROGRESS.