ATX X HAD NMAC LTSS FROM Y. SYS ERROR. EVASIVE ACTION TAKEN.

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ATX X CONTACTED CHA APCH APPROX 30 DME FROM THE CHA VOR AT 11000 FT. CHA GAVE US 7000 FT AND SHORTLY THEREAFTER; A 070 DEG HDG FOR THE VISUAL FOR RWY 20. AT THIS TIME; WE HEARD A BARON REQUEST RWY 33 AND THEN ASK IF IT WOULD BE A PROB. APCH ANSWERED IN THE NEGATIVE. APPROX 12 MI FROM THE ARPT; THE FO REQUESTED LOWER AND WE WERE GIVEN 4000 FT. AT APPROX 7 MI FROM THE ARPT; STILL ON THE 070 DEG HDG; CHA GAVE US 3500 FT AND THE FO CALLED THE ARPT IN SIGHT. APCH CTL CLRED US FOR THE VISUAL APCH FOR RWY 20 AND SHORTLY AFTERWARDS; HANDED US OFF TO TWR. WHEN WE SWITCHED TO TWR FREQ; WE OVERHEARD TWR TELL THE BARON TO TURN HIS BASE LEG NOW. THE FO CHKED WITH TWR FOR THE VISUAL RWY 20 AND WE WERE TOLD WE WERE #2 BEHIND A BARON ON THE APCH FOR RWY 33; A XING RWY. THE FO REPLIED THAT WE WOULD SLOW IT DOWN AS BEST WE COULD. AT APPROX 500 FT AGL; TWR SAID; 'THIS ISN'T WORKING OUT;' AND INSTRUCTED US TO 'START A CLBING R TURN.' WE WERE NOT TOLD TO GAR. TWR THEN SEEMED TO FORGET ABOUT US. AFTER CLBING FOR ABOUT 1600 FT IN A SLOW R TURN; CLBING THROUGH 3100 FT MSL; AND A HDG OF 250 DEGS; I REQUESTED A HDG AND ALT. WE WERE GIVEN 3500 FT AND A HDG OF 250 DEGS. WE THEN STARTED GETTING VECTORS OF ABOUT 30 DEGS HDG CHANGE FOR EACH VECTOR UNTIL WE WERE ROUGHLY PARALLELING RWY 2-20 ON AN APPROX HDG OF 330 DEGS. SHORTLY AFTER GETTING THE VECTOR OF 330 DEGS; WE WERE GIVEN TFC Y AT 1 O'CLOCK AND LESS THAN A MI. I SPOTTED A CESSNA 210 AT 1 O'CLOCK AT APPROX 1/4 TO 1/2 MI AND 300 FT. I PITCHED UP AND THE CESSNA PASSED DIRECTLY BELOW US. I POINTED OUT THE CESSNA TO THE FO AND HE RPTED IT IN SIGHT. WE WERE TOLD TO MAINTAIN VISUAL SEPARATION AND GIVEN 2500 FT. WE THEN FOLLOWED A SABRE JET FOR THE VISUAL RWY 20; NORMAL APCH AND LNDG. THE SAAB SF-340B I FLY IS A 30 PAX; PART 135 ACFT WITH NO TCASII.