POTENTIAL CONFLICT BTWN A BE02 AND A CITATION JET WITH CONVERGING HEADINGS AFTER TKOF AT PHX ARPT. BE02 TCASI ALERTED FLC OF XING TFC. ONLY THEN; AFTER A TURN WAS MADE TO PARALLEL THE COURSE OF THE CITATION DID ATC ADVISE OF TFC AND CHANGE THE BE02'S ALT ASSIGNMENT. RPT INDICATES EITHER A CTLR PROB OR A RADAR DISPLAY PROB.

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ACFT #1 WAS ASSIGNED A HDG OF 340 DEGS TO JOIN V327 (359 DEG RADIAL PXR) AND TO CLB FROM 5000 FT MSL TO MAINTAIN 13000 FT MSL. WHEN CLBING THROUGH APPROX 7700 FT MSL; ACFT #1'S TCASI ALERT SOUNDED. THE PF OF ACFT #1; SAW ACFT #2 OUT THE R WINDOW AT THE ESTIMATED DISTANCES STATED HERE-IN. UPON FIRST SIGHTING OF ACFT #2; ACFT #1 WAS TURNED SO AS TO PARALLEL ACFT #2'S COURSE. AT THIS TIME; ATC ASSIGNED ACFT #1 AN ALT OF 8000 FT MSL. AT NO TIME DID ATC TELL EITHER ACFT OF A CONFLICT. WHEN ACFT #2 PASSED IN FRONT OF ACFT #1 WITH AN APPROX VERT SEPARATION OF 1000 FT; ATC INFORMED ACFT #1 THAT ACFT #2 HAD 'PASSED BEHIND.' THE OBVIOUS RESOLUTION TO THIS EVENT IS GOOD PLT TFC VIGILANCE. ALTHOUGH BOTH ACFT WERE IFR AND UNDER ATC CTL; EXTRA VIGILANCE ON BOTH PARTIES' PARTS COULD POSSIBLY HAVE MADE THIS ENCOUNTER OCCUR A LITTLE FARTHER APART. SUPPLEMENTAL INFO FROM ACN 380901: CITATION DEPARTED PRIOR TO US OUT OF PHX. THEY WERE APPROX 3-4 MI AHEAD OF US ON OUR DEP. CITATION WAS GIVEN A NW VECTOR TO INTERCEPT THE DRAKE 6 DEP; WHILE WE WERE GIVEN A N TO NNW VECTOR TO INTERCEPT THE 359 DEG RADIAL OUT OF PHX. ALT CLRNC WAS 4000 FT THEN TO 5000 FT. LEVELED AT 5000 FT; DEP CLRED US UP TO 13000 FT. APCHING 8000 FT; WE RECEIVED A TA FROM TCASI WHICH POINTED OUT ACFT AT 1 O'CLOCK POS AND LESS THAN 1000 FT ABOVE US. OUR RATE OF CLB AT THE TIME OF TA WAS 3000 FPM. EVASIVE MANEUVERS CONSISTED OF LEVELING AT APPROX 7700-7800 FT ALT AND A L APPROX 30 DEG HDG CHANGE; AS PATHS WERE CONVERGING. WE ADVISED ATC WE THEN HAD ACFT Y IN SIGHT. AFTERWARDS; ATC RECLRED US TO 13000 FT. CONSIDERATIONS IN THIS EVENT: POSSIBLE MISSED TA FROM ATC? WORKLOAD OF ATC AND OF FLC. POSSIBLE ACCURACY OF RADAR EQUIP? NOTE: AFTER WE ADVISED ATC WE HAD ACFT IN SIGHT AND CLRED TO 13000 FT; ATC ADVISED THE CITATION WAS 'PASSING BEHIND AND ABOVE YOU; SHOULD BE NO FACTOR;' WHEN ACTUALLY THE ACFT WAS STILL IN FRONT AND ABOVE US (1 O'CLOCK POS MOVING TO 11 O'CLOCK POS).