CORP LTT HAS NMAC WITH SECOND LTT. CTLR HAVE GIVEN VECTOR TO SEPARATE.

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ACFT WAS ON A 090 HDG; UNDER RADAR CTL OF COLORADO SPRINGS DEP CTL. OUR ACFT HAS TCASII AND WE HAD NOTICED TFC AHEAD WHOSE ALT WE WOULD PASS THROUGH. ATC GAVE US A 080 HDG AND ADVISED THAT THE TFC SHOULD PASS TO OUR R. THE TCASII ADVISED TFC! I LOOKED UP TO SEE AN LTT XING OUR NOSE AT APPROX THE SAME ALT. I INITIATED A RAPID CLB WHICH CAUSED THE PAX TO CRY OUT IN THE BACK 'WHOA.' AS I INITIATED THE PULL UP THE TCASII ADVISED TO INCREASE THE CLB RATE BY ADVISING 'MONITOR VERT SPD' AND SHOWING A 2500 FPM RATE OF CLB. AFTER WE WERE CLR OF CONFLICT DEP ANNOUNCED THAT SHE HAD JUST NOTICED THAT THE TFC HAD TURNED ACROSS OUR NOSE; THIS CALL WOULD HAVE BEEN A LITTLE LATE HAD ONE OF US NOT HAD OUR EYES OUT OF THE COCKPIT AND HAD WE NOT HAD TCASII. I FIND THAT INCREASINGLY IN BUSY TERMINAL AREAS WITH A LOT OF VFR TFC WE GET MORE AND MORE TFC ADVISORIES THAT ARE BACKED UP BY VISUAL SIGHTINGS. I WONDER IF ATC KNOWS THAT WE HAVE TCASII AND IS THEREFORE LEAVING IT UP TO US TO AVOID VFR TFC THAT IS IN CONFLICT. I HAVE HAD 2 SIMILAR OCCURRENCES AT PEACHTREE DE KALB ARPT OUTSIDE ATLANTA; BUT THIS IS THE CLOSEST WE HAVE COME WHILE UNDER RADAR CTL.