A PVT PLT HAS AN NMAC WHILE TRYING TO LAND AT HPN.

Narrative

AT APPROX XA30 I ANNOUNCED MYSELF TO THE WESTCHESTER COUNTY TWR. WESTCHESTER COUNTY TWR INSTRUCTED ME TO RPT MID DOWNWIND FOR LNDG RWY 29. I REPEATED THE INSTRUCTION. AFTER A FEW MINS; I NOTICED SEVERAL ACFT IN THE AREA AND MUCH RADIO CHATTER AND WANTED TO VERIFY MY POS AND INTENT. I ASKED WESTCHESTER COUNTY TWR IF I COULD CROSS MID FIELD AND ENTER RWY 29 FROM A R PATTERN. THIS SEEMED TO BE A SAFER APCH GIVEN THE TFC AHEAD OF ME. WESTCHESTER COUNTY TWR THEN INDICATED THAT WOULD NOT BE PERMITTED; TO STAND BY FOR RESEQUENCING. I REPEATED STANDING BY. WESTCHESTER COUNTY TWR THEN ASKED IF I SAW THE CESSNA ON BASE FOR RWY 34 AHEAD OF ME. I RESPONDED THAT I HAD THE ACFT IN SIGHT. WESTCHESTER COUNTY THEN INSTRUCTED ME TO FOLLOW THE ACFT IN AND THAT I WAS CLRED TO LAND RWY 29. I FOLLOWED THE ACFT AND OBSERVED IT AS IT BEGAN ITS DSCNT FOR LNDG RWY 34. I WAS ABOUT TO START MY DSCNT FROM TPA 1500 FT MSL WHILE ON L BASE FOR RWY 29; WHEN I NOTICED AN ACFT CONVERGING ON MY POS FROM MY REAR L QUARTER; APPARENTLY AT THE END OF DOWNWIND ON RWY 34. IMMEDIATELY I ADDED FULL PWR AND VEERED TO THE L HEADING NE. I IMMEDIATELY NOTIFIED TWR THAT I WAS CONTINUING NE TO AVOID TFC AND WOULD BE ENTERING RWY 29 FROM A R BASE. I THEN HEARD THE OTHER ACFT ANNOUNCE TO WESTCHESTER COUNTY TWR THAT A SINGLE ENG ACFT HAD CROSSED ITS FLT PATH; MEANING MY ACFT. AFTER COMPLETING MY R BASE TURN AND ENTERING FINAL; WESTCHESTER COUNTY TWR CLRED AN ACFT FOR TKOF FROM RWY 34. I THEN NOTIFIED WESTCHESTER COUNTY TWR THAT I WAS ON FINAL. WESTCHESTER COUNTY TWR CLRED ME FOR LNDG RWY 29. I REPEATED CLRNC TO LAND RWY 29 AND DID SO.