MID WING SMA HAS NMAC WITH CLBING B737 AND TAKES EVASIVE ACTION. B737 FLC RPTS AN ACFT DOVE IN FRONT OF THEM.

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I WAS TRANSITIONING THROUGH LAS AIRSPACE; LEVEL AT 10500 FT MSL; ON AN APPROX HDG OF 280 DEGS; SSW OF THE FIELD. ATC NOTIFIED ME OF A CLBING TFC OFF MY R WING AND WAS TOLD HE WAS CLRED TO 10000 FT. I RPTED I HAD THE TFC IN SIGHT -- IT WAS A B737. HE STARTED TO TURN TOWARDS ME; STILL IN A CLB AND WAS CLOSING ON ME WITH AN IMPRESSIVE SPD ON A PERFECT COLLISION COURSE. HE WAS SUPPOSED TO LEVEL BELOW. AT THIS POINT; I TURNED ON MY SMOKE SYS HOPING HE WOULD NOTICE ME (SEE AND BE SEEN?) STILL AT 10500 FT. AT THIS POINT; HE APPEARED TO CONTINUE TO CLB AFTER FLYING THROUGH HIS ASSIGNED ALT. I HAD NO CHOICE AT THIS TIME TO TAKE EVASIVE ACTION AND TO PUSH DOWN HARD AND MAKE A R TURN (NOT BEING ABLE TO OUTCLB OR OUTRUN A B737); TO AVOID A POSSIBLE COLLISION. IT WAS MY ONLY OPTION. IT SEEMS THAT HE FINALLY SAW ME; AND CONTINUED TO CLB; AND HE RPTED THAT I WAS AT 10000 FT; AND DOVE RIGHT IN FRONT OF HIM. AS SOON AS I LEVELED OFF BACK AT 10500 FT; I REQUESTED AN ALT CHK AND ATC HAD ME AT 10600 FT. ATC ASKED ME WHY I DIDN'T RPT MY ALT CHANGE. MY REPLY WAS OBVIOUS -- THERE WAS NO TIME; I WAS BUSY TRYING TO AVOID A B737. I DIDN'T LOSE SIGHT OF THE TFC FROM THE TIME IT WAS RPTED TO ME. I WENT BY ONE OF THE MOST IMPORTANT SAFETY RULES -- SEE AND AVOID. AND IF HE WOULD HAVE BEEN WHERE HE WAS SUPPOSED TO BE; IT WOULD HAVE BEEN SUICIDAL FOR ME TO DIVE FROM 10500 FT TO GO UNDERNEATH HIM. THE CREW OF THE B737 WAS PROBABLY BUSY IN THEIR COCKPIT AND FAILED TO LOOK OUT AND MISSED THEIR ASSIGNED ALT. MAYBE IF ATC WOULD HAVE GIVEN US MORE VERT SEPARATION; THIS MIGHT NOT HAVE HAPPENED.