MD80 CREW HAD AN NMAC WHILE FLYING THE 4 STACKS CHARTED VISUAL APCH INTO BUR.

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TCASII SAVE. WE WERE CLRED FOR THE FOUR STACKS VISUAL APCH TO RWY 15 AT BUR. THE FO WAS FLYING. WE TURNED FINAL JUST ABOUT 3000 FT; AND ON A GOOD GLIDE PATH WHEN TWR POINTED OUT TFC AT OUR 2 O'CLOCK POS; ORBITING AT 2100 FT JUST N OF THE APCH COURSE. WE TOLD HIM WE WERE LOOKING; AND CONTINUED DSCNT AT ABOUT 800 FPM; IN THE PROCESS OF CONFIGURING. I CONTINUED TO LOOK FOR THE RPTED TFC AS I COULD SEE HIM ON THE TCASII DISPLAY; AND IT APPEARED OUR COURSES WERE CONVERGING AND WE WERE DSNDING TOWARD HIS ALT. WE NEVER ACQUIRED THE TARGET VISUALLY; BUT RECEIVED A TFC ALERT WHICH RAPIDLY BECAME AN RA OF 'MONITOR VERT SPD' AND IT DISPLAYED TO LEVEL AT 200 FPM CLB GREEN ARC. I INSTRUCTED THE FO TO RESPOND IMMEDIATELY (LEVELOFF OR CLB) WHICH HE DID. PERHAPS 1 SECOND LATER; THE RA CHANGED TO 'CLB; CLB NOW' AND WE BEGAN TO ROTATE FOR A GAR/CLB AS REQUIRED; WITH THE TCASII COMMANDING A CLB RATE OF 2000 FPM. 2 SECONDS LATER; IT BECAME A CLR OF CONFLICT. I HAVE IMBEDDED IN MY MEMORY THAT THE RED BOX SHOWED 200 FT BELOW US; WITH THE SYMBOL IN CONTACT WITH OUR ACFT SYMBOL WITH THE DISPLAY ON THE 5 MI RANGE. THERE WAS A BLIP ON THE RADIO ALTIMETER; WHICH WAS ALREADY ALIVE; BUT ONLY FOR A FLASH. BUR TWR CALLED ABOUT THAT TIME AND ASKED IF WE THOUGHT WE WOULD BE ABLE TO GET DOWN FROM OUR PRESENT POS; AND THIS BEING THE FIRST FREE MOMENT I HAD; I EXPLAINED THAT WE WERE IN THE PROCESS OF GOING AROUND; THAT WE'D HAD AN RA; AND COULD NOT LAND OUT OF THE APCH. HE EXCITEDLY SAID 'I CALLED THAT TFC OUT TO YOU;' TO WHICH I RESPONDED THAT HE HAD; BUT WE NEVER SAW HIM AND WE'D RECEIVED THE RA AND HAD RESPONDED. WE THEN STAYED WITH TWR FOR A R DOWNWIND VISUAL TO RWY 8. IT'S ONLY IN FILLING OUT THE TCASII SURVEY AFTER THE FACT THAT I REALIZE HOW VERY CLOSE THIS EVENT MAY HAVE BEEN. AT THE TIME; IT WAS A MATTER OF RESPONDING; AND SUBSEQUENT DUTIES; ETC; THAT DELAYED MY DETAILED RECOUNTING OF THIS EVENT. BUT I CAN VERY VIVIDLY RECALL IN DETAIL THE PROGRESS OF OUR TARGETS CLOSING; AND THE RELATIVE DISTANCE IN ALT; AND I FEEL THAT HAD IT NOT BEEN FOR THE TCASII SYS; WE COULD VERY WELL HAVE HIT THIS SMALL ACFT; AND THAT THE OTHER ACFT WAS ON THE FINAL APCH COURSE; THOUGH ABOUT 7 MI FROM THE FIELD; SO PROBABLY OUTSIDE THE ATA. BEING ON A VISUAL APCH; AND HAVING TWR CALL OUT THE TFC; CERTAINLY PRIMED ME FOR ESCAPING FROM THE SIT; BUT THE TCASII DISPLAY AND SUBSEQUENT ADVISORIES WERE AN IMMEASURABLE AID.