POTENTIAL CONFLICT BTWN A C414A AND A XING B737-400 WITH BOTH FLC'S SUPPOSEDLY MAINTAINING VISUAL SEPARATION FROM EACH OTHER ON FREQ WITH APCH CTLR AT SCK; CA.

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VFR CHARTER FLT FROM SALINAS TO SACRAMENTO EXECUTIVE AND LINCOLN; CA. RECEIVING RADAR ADVISORIES FROM STOCKTON APCH AT 8500 FT. MY FLT PATH WOULD TAKE US ACROSS THE VERY BUSY ARRS INTO THE BAY AREA. I NORMALLY CROSS THIS AREA AT A LOWER ALT; BUT BECAUSE OF TURB OVER THE MOUNTAINS; I CONTINUED AT 8500 FT MSL. UPON INITIAL CONTACT WITH APCH; I WAS TOLD TO INFORM HIM BEFORE I BEGAN A DSCNT TO SACRAMENTO. HE ALSO POINTED OUT AN ACR B737 XING FROM R TO L. I ACKNOWLEDGED THAT I HAD VISUAL CONTACT WITH THAT TFC. I ALSO SAW THE FOLLOWING ACFT. APCH INFORMED ME THAT THE ACFT WOULD BE DSNDING TO 8000 FT AND THE CREW RPTED THEY HAD MY ACFT IN SIGHT. AS I CONTINUED ON MY COURSE AND ALT THE OTHER ACFT (ACR Y FLT) APPEARED TO BE DSNDING TOWARD MY ACFT ON A COLLISION COURSE. I ANTICIPATED THAT HE WOULD DSND BELOW MY FLT PATH; BUT AS HE CLOSED WITHIN 1 MI HE STILL APPEARED TO BE ABOVE US IN A DSCNT. I DECIDED IT WAS TIME TO EXERCISE MY EMER AUTH ACCORDING TO FAR 135.19 AND BEGAN A CLBING L TURN OUT OF HIS WAY. AS I TURNED L TO A COURSE THAT WAS 90 DEGS TO ACFT Y'S FLT PATH; MY R SEAT PAX SAID THE OTHER ACFT STARTED A R CLBING TURN. ATC THEN ASKED IF I HAD THE OTHER ACFT IN SIGHT. I REPLIED THAT I WAS HEADING S (90 DEGS AWAY FROM HIS FLT PATH) AND NO LONGER SAW HIM. ATC ASKED IF I WAS STILL GOING TO SACRAMENTO. I REPLIED THAT I WAS AND TURNED BACK ON THE ORIGINAL COURSE AND ALT. BY THIS TIME THE NEXT ARR TFC WAS POINTED OUT APCHING FROM THE R. ATC ASKED IF I WOULD LIKE TO DSND TO 7500 FT. I REPLIED THAT I WOULD AND THAT THE OTHER TFC WAS IN SIGHT. AS I DSNDED; ATC GAVE A PHONE NUMBER TO BOTH FLT Y AND TO ME. WE ARE BOTH TO FILE AN NMAC RPT. UPON ARR AT LINCOLN; I PHONED STOCKTON TRACON AND RPTED TO THE SUPVR. HE ASKED IF MY ACFT WAS EQUIPPED WITH TCASII. I REPLIED IT WAS NOT. HE TOLD ME THAT ACR FLT Y HAD LEVELED OFF AT 9000 FT AND WAS GOING TO MAINTAIN 9000 FT UNTIL HE PASSED ME. I TOLD HIM I NEVER HEARD THE CREW OR ATC STATE THAT AND IF I HAD REALIZED HE WAS MAINTAINING 9000 FT; I WOULD NOT HAVE CLBED. I STILL WOULD HAVE TURNED OUT OF HIS WAY. I FEEL THAT IF HE PLANNED TO CROSS 500 FT OVER THE TOP OF MY ACFT WE WOULD STILL BE TOO CLOSE. SINCE; I ASSUME; ACR FLT Y HAD TCASII THEY WOULD HAVE RECEIVED A FLY-UP COMMAND WHEN I STARTED A CLBING TURN. FROM OUR VISUAL PERSPECTIVE; BOTH MY R SEAT PAX AND I PERCEIVED THE ACFT Y IN A DSCNT UNTIL HE PULLED UP AND TURNED R. I DO NOT KNOW ATC'S TFC SIT AT THE TIME; BUT A LOWER ALT OR A VECTOR AWAY FROM THE OTHER ACFT FLT PATH MIGHT HAVE PREVENTED THE NEED FOR EVASIVE MANEUVERING. SUPPLEMENTAL INFO FROM ACN 547314: ON MARVIN 1 ARR TO OAK AT 9000 FT; WE WERE INFORMED OF TFC AT 10 O'CLOCK POS; APPROX 5 MI AT 8500 FT. WE RPTED 'TFC IN SIGHT' AND WERE DIRECTED 'REF THAT TFC; CROSS CATTY INTXN AT 8000 FT.' WE DID NOT BEGIN DSCNT DUE TO THE POS OF THE OTHER ACFT. SHORTLY THEREAFTER; THE OTHER ACFT BEGAN WHAT APPEARED TO BE A CLBING R TURN. WE BEGAN A CLBING R TURN TO AVOID COLLISION; CLBING TO 10000 FT. TCASII DID NOT GIVE AN RA; MOST LIKELY DUE TO OUR EVASIVE MANEUVER. THE OTHER ACFT BEGAN A DSNDING L TURN AND WE RETURNED TO OUR CLRED ROUTING AND ALT. WE LANDED AT OAK WITHOUT FURTHER INCIDENT.