AFTER TKOF RWY 35R APA THE PLT REQUESTED A L TURN WHICH WAS APPROVED AND ASSIGNED ANOTHER FREQ AND CTLR AT APA. WHILE IN CONTACT WITH AND COMPLYING WITH THAT CTLR'S INSTRUCTIONS THE PAX ALERTED THE PLT TO AN IMMINENT COLLISION WITH ANOTHER ACFT. AN EVASIVE ACTION CLB AND TURN AVOIDED THE OTHER ACFT. THE OTHER ACFT MADE AN EVASIVE MANEUVER ALSO. THE CTLR TOLD THE RPTR TO IDENT; THE TFC WAS NO FACTOR; AND THE RPTR SHOULD NOT HAVE CHANGED TO HIS FREQ. THE OTHER TFC WAS FROM DEN.

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I WAS CLRED TO TKOF FROM APA'S RWY 35R FOR A N DEP. I READ BACK THE CLRNC AS I TAXIED ONTO THE RWY AND PROCEEDED TO TKOF. BY THE END OF THE RWY I WAS ABOUT 400- 500 FT AGL AND CALLED ATC TO ASK IF A L TURN WOULD BE APPROVED FOR A NW HDG. ATC CALLED BACK WITH THE OK AND TOLD ME TO CHANGE FREQ TO ANOTHER CTLR AT APA THAT WAS HANDLING TFC FOR RWY 35L. I REPEATED THE FREQ AND CALL NUMBERS AND THE CTLR VERIFIED. I IMMEDIATELY SWITCHED FREQ AND MADE THE INITIAL CALL TELLING HIM THAT I WAS WITH HIM. HE THEN ASKED ME FOR MY POS. I TOLD HIM THAT I WAS OVER BELLVIEW (RD) AND HE TOLD ME TO FLY TOWARD I-25 (W) AND THEN ON COURSE. SO I FLEW PARALLEL TO BELLVIEW UP TO I-25 AND THEN N. ABOUT 3 1/2 - 4 MI FROM THE DEP END OF RWY 35R THE NEAR MISS OCCURRED. MY PAX WAS THE FIRST TO SEE THE OTHER ACFT. THE REASON WHY I DIDN'T SEE THE OTHER ACFT BEFORE MY PAX IS BECAUSE THE ACFT WAS HIDDEN BEHIND THE PANEL THAT IS IN BTWN THE WINDSHIELD AND THE L SIDE DOOR. MY PAX POINTED TO MY L SO I MOVED MY HEAD FORWARD TO SEE WHAT SHE WAS POINTING AT. THE ACFT WAS A SMALL 2-4 SEAT SINGLE-ENG LOW WING PLANE WITH FIXED GEAR. I IMMEDIATELY PUSHED DOWN AND TOWARD THE R AS SOON AS I RECOGNIZED THE ACFT WAS MOVING DIRECTLY AT US. I ALSO NOTICED THAT THE OTHER ACFT MOVED UP AND TO THE R AT THE SAME TIME AS MY MANEUVERING OF THE ACFT. THEN I NOTIFIED ATC OF THE NEAR MISS TELLING THEM THAT IT CAME WITHIN 20- 50 FT FROM HITTING ME. HE TOLD ME TO IDENT; WHICH I DID. THE CTLR THEN TOLD ME THAT TFC WAS NO FACTOR AND THAT I SHOULD NOT HAVE CHANGED TO HIS FREQ AFTER TKOF. HE SAID THAT I PROBABLY MISUNDERSTOOD THE CALL OR MISTAKEN THE CALL NUMBERS OF A DIFFERENT ACFT. BUT I WAS AWARE OF THE OTHER ACFT WITH SIMILAR CALL NUMBERS AND PURPOSELY VERIFIED ALL CLRNCS WITH MY CALL NUMBERS (MINE WAS HCC AND THE OTHER WAS SOMETHING LIKE HDC). THEY ALSO TOLD ME THAT THE TFC WAS DEN AND NOT APA AND THEN HANDED ME OFF FOR DEN APCH. I TOLD THEM WHAT HAPPENED AND THEY TOLD ME THAT THEY WOULD CALL APA TO CHK TO SEE IF ANY RPTS WERE FILED. THAT WAS THE LAST I HEARD OF IT. I REALIZED THROUGH THIS SIT THAT ATC SHOULD NOT BE RELIED ON FOR TA'S UNLESS ON AN IFR FLT PLAN. I SHOULD ALSO MAKE SURE I CAN SEE EVERYTHING FROM MY SEAT; EVEN IF IT MEANS MOVING AROUND ONCE IN AWHILE. I WOULD HATE TO THINK WHAT WOULD OF HAPPENED IF I WERE FLYING ALONE THAT TRIP! THE ONLY THING THAT MIGHT HELP THIS OCCURRENCE FROM HAPPENING AGAIN WOULD BE FOR ATC TO USE THEIR RADAR MORE OFTEN. I THINK APA SHOULD BE RECLASSIFIED TO CLASS C. THE TFC VOLUME HAS INCREASED INCREDIBLY SINCE THE OPENING OF DENVER INTL ARPT (MOSTLY COMMERCIAL OR CORPORATE JETS).