MOONEY 20C PLT HAS A CLOSE ENCOUNTER WITH ANOTHER ACFT DURING ENTRY INTO THE TFC PATTERN AT LVK.

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I WAS APCHING LVK FROM THE N AND WAS INSTRUCTED BY THE TWR TO RPT 2 MI R BASE FOR RWY 25R. WHEN I REACHED THAT POINT; I RPTED MY POS AND WHILE ON THE RADIO WITH LVK TWR I HAD TO TAKE EVASIVE ACTION TO AVOID A NBOUND CESSNA AT THE SAME ALT; 1400 FT MSL. THE CESSNA HAD BEEN RPTED TO ME AT MY INITIAL CALL TO BE MANEUVERING OVER THE 'JUMP ZONE.' THIS IS AN INEXACT AREA WITHIN THE LVK CLASS D AIRSPACE APPROX 3 MI TO THE E OF THE CONFLICT SITE. I HAVE BEEN BASED AT LVK FOR SOME 25 YRS AND I KNOW APPROX WHERE THE 'JUMP ZONE' WAS. WHEN IT WAS IN USE THERE WAS A DIRT STRIP THERE. IT HAS NOT BEEN USED FOR MANY YRS AND I CANNOT PINPOINT IT FROM THE AIR NOW. I HAD 2 CONVERSATIONS WITH TWR PERSONNEL WHO TELL ME THEY DON'T HAVE ANYTHING ON PAPER TO IDENT THE LOCATION OF THE 'JUMP ZONE' DEFINITIVELY. I QUESTIONED WHETHER IT WAS SAFE FOR ACFT TO PRACTICE GND REF MANEUVERS INSIDE THE CLASS D AIRSPACE AND WAS ADVISED BY THE ACTING TWR CHIEF THAT THIS WAS COMMON AT LVK AND HWD AND THERE WAS NOTHING THE FAA TWR COULD DO ABOUT IT.