NMAC BTWN TO SMA SEL ACFT IN A CTLED TFC PATTERN FOR 2 DIFFERENT RWYS AND OPPOSITE DIRECTION PATTERNS.

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FLYING INBOUND FROM THE E TO LAND IN HVN; CONTACTED TWR 10 MI OUT TO INSTRUCTION. WAS TOLD TO CALL BACK ON 4 MI; PLAN L TFC FOR RWY 14. CALLED INBOUND 4 MI OUT; TWR SAID TO RPT ENTERING L DOWNWIND FOR RWY 14. UPON REACHING ARPT TFC PATTERN I JOINED L DOWNWIND ON THE 45 DEG ENTRY FOR RWY 14. TWR ADVISED ME I HAD TFC ON R DOWNWIND FOR RWY 20; TOUCH AND GO. I STATED I HAD NO VISUAL CONTACT WITH RPTED TFC. AT THAT TIME THE ACFT PASSED APPROX 100 FT UNDER MY ACFT FLYING IN THE OPPOSITE DIRECTION. AFTER A NEAR MISS; I STATED; 'UNBELIEVABLE' ON THE TWR FREQ. TWR ADVISED ME IT WAS 'SEE AND AVOID' ON VFR. THE OTHER ACFT STATED 'TFC NO FACTOR' AFTER THE FACT OF THE NEAR MISS. I WAS CLRED TO LAND AND DID SO IMMEDIATELY. ONCE ON THE GND I CONTACTED THE TWR BY PHONE TO HAVE HIM EXPLAIN HIS PERCEPTION OF THE INCIDENT. TWR MGR STATED IT WAS VFR; 'SEE AND AVOID.' IN MY OPINION AN ALT REQUEST FROM BOTH ACFT WOULD HAVE BEEN EXTREMELY HELPFUL WHEN I STATED NO VISUAL CONTACT OF THE OTHER ACFT; INSTEAD OF SAYING 'SEE AND AVOID.' A REQUEST FOR ONE OF US TO DO A 360 DEG TURN FOR SPACING WAS ANOTHER OPTION.