NMAC BTWN A SOCATA TRINIDAD TB20 (TB20) SIGHTSEEING OVER THE CITY OF SAT AND A C172 XING OVER THE TOP OF THE TB20. APCH CTL HAD ISSUED AN ADVISORY OF THE TFC AND THEN RECOMMENDED A TURN. RPTR IN THE TB20 IMMEDIATELY TURNED AND DSNDED IN ORDER TO AVOID A COLLISION.

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WX WAS FORECAST 2500 FT BROKEN; 7 MI VISIBILITY. INFLT RPTED 3100 FT BROKEN. THERE WAS SOME HAZE. PERSON IN THE R SEAT OF MY ACFT WAS A CFI. PRIOR TO DEP FROM KELLY AFB; I REQUESTED PERMISSION FOR VFR SIGHTSEEING OVER DOWNTOWN SAN ANTONIO. I WAS GIVEN A SQUAWK AND TOLD TO FLY RWY HDG AND REMAIN VFR BELOW 3000 FT. ON DEP I WAS TURNED OVER TO SAN ANTONIO APCH WHO CLRED ME TO A L TURN; ON COURSE. DURING CLBOUT; SAN ANTONIO ASKED ME IF I COULD CLB TO 2500 FT TO REMAIN CLR OF STINSON AIRSPACE. I REPLIED THAT I WOULD CLB UP TO SEE IF IT WAS VFR AT 2500 FT. IT WAS. AFTER ESTABLISHING A L-HAND TURN OVER DOWNTOWN; THE FIRST TFC RPT I CAN RECALL IS APCH TELLING THE C172 MY RELATIVE POS AND ALT. I DON'T RECALL WHAT THE POS WAS; BUT HE DID SAY I WAS INDICATING 2300 FT. MY ALTIMETER SHOWED 2500 FT. THE FIRST CALL TO ME; THAT I CAN RECALL; WAS VFR TFC; 10 O'CLOCK; 1 MI. I ROGERED AND SAID I WOULD TIGHTEN MY TURN. THE CTLR REPLIED HE THOUGHT IT WOULD BE BETTER IF I TURNED R. AS I ROLLED WINGS LEVEL PRIOR TO TURNING R; I SPOTTED THE C172; SLIGHTLY ABOVE ME AT APPROX 1/2 MI; 12 O'CLOCK; MOVING FROM MY L TO MY R. I IMMEDIATELY ROLLED BACK INTO A L TURN AND PUSHED OVER. AFTER INITIATING EVASIVE ACTION; I ATTEMPTED TO CALL APCH TO LET HIM KNOW THAT I HAD THE TFC AND WAS MANEUVERING TO AVOID; BUT WAS PREEMPTED BY HIS CALL TO THE C172; SUGGESTING AN IMMEDIATE CLB ALONG WITH A TFC ALERT. WE MISSED EACH OTHER BY AN ESTIMATED 300-400 FT HORIZLY AND VERTLY.