AN ACR ACFT BEING VECTORED FOR A VISUAL APCH TO RWY 19L MISSED A TURN CLRNC AND HAD AN NMAC WITH A CESSNA. TCASII ALERTED THE ACR FLC AND THEY REACTED TO THE RA.

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ON FIRST CONTACT WITH LAS APCH CTL; I WAS TOLD WE WOULD BE LNDG ON RWY 19L. ABEAM THE ARPT; HDG 080 DEGS; I WAS SWITCHED TO ANOTHER CTLR WHO TURNED ME DOWNWIND. WE WERE AT 6000 FT. OVERHEAD THE FIELD I WAS HANDED OFF TO A THIRD CTLR; WHO CLRED US TO 5000 FT. APPROX 3 NM BEYOND THE APCH END OF RWY 19L; TFC OUR SEQUENCE WAS POINTED OUT TO ME AS A B737 ON A '3 MI FINAL; COULD WE MAKE IT FROM THERE?' I CALLED THE TFC AND SAID WE COULD. THE NEXT RADIO CALL I HEARD WAS EITHER GARBLED OR STEPPED ON. AT THIS POINT; A CONTINUOUS CONVERSATION BEGAN BTWN THE CTLR AND A CESSNA. I ATTEMPTED TO BREAK IN SEVERAL TIMES TO ASK IF WE WERE CLRED THE VISUAL; AS AT THIS POINT IN TIME; I HAD NOT RECEIVED; NOR ACKNOWLEDGED A CLRNC FOR A VISUAL APCH. THIS WENT ON FOR ABOUT 1 MIN. EVEN THOUGH TCASII HAD SHOWED NO TFC; OR TA'S; WE RECEIVED AN 'INSTANTANEOUS' RA 'CLB; CLB' WITH A 2500 FPM CLB COMMANDED BY TCASII. AT THIS POINT WE WERE AT AROUND 5500 FT. I TOOK CTL AND ANSWERED THE RA WITH AN AGGRESSIVE CLB. I SAW A CESSNA PASSING DIRECTLY UNDER US; HDG FOR THE ARPT. HE APPARENTLY HAD NOT SEEN US. APCH FINALLY CALLED US AND SAID; 'IF WE HAD TURNED TO A 240 HDG AS HE HAD TOLD US TO DO;' THERE WOULD NOT HAVE BEEN A CONFLICT. I TOLD HIM IN WORDS TO THE EFFECT THAT I HAD NOT RECEIVED THE CALL NOR ACKNOWLEDGED IT. PROBS: 1) TOO MANY FREQ CHANGES IN CLOSE. IT DID NOT ALLOW A PLT TO BUILD SITUATIONAL AWARENESS AS TO WHAT THE 'BIG PICTURE' WAS. 2) APCH TRYING TO WORK ACR TFC INTO WHAT IS NORMALLY A GA PATTERN. THE RWYS 25 WERE ACTIVE AND THE WIND FAVORED EITHER ONE. 3) APCH NEVER CALLED THE CESSNA TFC TO US; YET HE DSNDED US INTO HIM; WITH MINIMAL LATERAL SEPARATION; ON OPPOSING HDGS AND THE SAME ASSIGNED ALTS. 4) APCH NOT LISTENING FOR CLRNC ACKNOWLEDGEMENTS; NOR LEAVING ANY OPEN FREQ TIME FOR CALLS.