AN EXPERIMENTAL ACFT PVT PLT HAS AN NMAC WITH A B737 WHILE XING THE APCH RTE TO OAK ARPT AT OR NEAR 4000 FT. ESE OF OAK; CA.

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AFTER DEPARTING PAO RWY 30 WITH A R TURN OUT AT THE DUMBARTON BRIDGE; I PROCEEDED ON A COURSE NNE TOWARD LVK ARPT. I STAYED UNDER 2000 FT UNTIL I CROSSED THE WATER (BAY) THEN CLBED TO GET ABOVE A LAYER OF MIST. AT 12:30 O'CLOCK POS MOVING TO MY 11 O'CLOCK POS; I ENCOUNTERED A COMMERCIAL AIRLINER AT APPROX MY ALT AND 1 MI AWAY -- CLOSING FAST. THE AIRLINER BANKED APPROX 70 DEGS TO THE R AND I DID THE SAME -- AN AGGRESSIVE CLB AND TURN TO MY R. SHORTLY THEREAFTER; PAO TWR RELEASED ME TO CONTACT CTR FOR FLT FOLLOWING. THERE WAS NO MENTION OF THE TFC BY PAO'S TWR TO ME. I IMMEDIATELY REQUESTED FLT FOLLOWING (VFR) FROM BAY APCH. THEIR CTLR SUBSEQUENTLY INFORMED ME THAT THEY OBSERVED ABRUPT CHANGES IN MY ALT (MODE C) BUT MADE NO MENTION OF THE POTENTIAL CONFLICT WITH AN AIRLINER. WHEN I ARRIVED IN SACRAMENTO AT SAC ARPT; I TOOK THE AIRPLANE IN TO HAVE THE XPONDER'S MODE C CHKED. NO PROB WITH MODE C. CONTRIBUTING FACTORS: 1) MIST BELOW APPROX 300 FT MSL. 2) CTR ASSUMED (MY OPINION) THAT MY MODE C WAS ERRATIC WHEN; IN FACT; I CLBED RAPIDLY TO GET ABOVE THE POOR VISIBILITY.