PA28 ON VECTORS FOR APCH HAS NMAC WITH TWIN OPPOSITE DIRECTION AND CLBING.

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ENRTE TO SAN FROM BULLHEAD CITY. WE WERE BEING VECTORED ABOVE AN AREA OF SAN DIEGO CALLED MISSION VALLEY; GIVEN VECTORS FOR SEQUENCING INTO SAN; BEHIND COMMERCIAL TFC. VMC; CAVU; ON A WEEKDAY. I WAS PIC; OTHER PLT WAS UNDER HOOD (GOGGLES) FOR CURRENCY FLT TRAINING. ATC WAS CALLING 2-3 TARGETS AS WE ENTERED CLASS B FROM NE. HOWEVER; A TARGET SUDDENLY APPEARED AT OUR 12 TO 1 O'CLOCK POS; WITHOUT ANY TFC CALL. IT WAS A LIGHT TWIN ACFT CLBING THROUGH OUR ALT; HEADING E; AND COMING RIGHT AT US. I GRABBED THE CTL AND MADE A SHARP L TURN TO AVOID THE ACFT. BALLPARK HORIZ CLRNC WAS 200 FT. NO CALL WAS EVER RECEIVED FROM ATC; NOR DID WE EVER TELL HER. HER SECTOR WAS NON-STOP CHATTER; AND SHE WAS IN CONSTANT COM WITH SOME ACFT. SHE WAS EXTREMELY BUSY. I KNOW THE OTHER ACFT NEVER SAW US. WITHOUT EVASIVE ACTION IT WOULD HAVE BEEN A FATAL INCIDENT. I BELIEVE THIS ACFT MIGHT/COULD HAVE JUST DEPARTED RWY 27 AT SAN; AND WAS EXECUTING A CLBING R TURN; THROUGH OUR ALT AND HDG. QUITE POSSIBLY THEY NEVER SWITCHED FROM CTL TWR TO ATC AFTER DEP TO GET TFC CALL (US); OR THEY EXECUTED TURN WITHOUT/PRIOR TO SWITCHING FREQS. WHO KNOWS?