B737 FLIGHT CREW MISTAKENLY BEGINS ITS TKOF ON RWY 09 AT BOS AS ACFT Z IS ALSO CLRED FOR TAKEOFF ON RWY 15R.

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TXWY V AT BOS; HOLDING SHORT OF RWY 09. THERE WAS A SAAB HOLDING SHORT AHEAD OF US; A DC-9 HOLDING SHORT ON TXWY S; S OF RWY 09; AND A B757 ON TXWY S; N OF RWY 09. THE SAAB WAS CLRED FOR TAKEOFF; I WAS THINKING WE WERE #3; AND DIRECTED THE FO TO COMPLETE THE BEFORE TAKEOFF CHKLIST. TWR CLRED US TO TAXI INTO POS AND HOLD ON RWY 09 AND WE ACKNOWLEDGED. WE WERE NOW #1; SO I CALLED BACK TO OUR LEAD FLT ATTENDANT TO HURRY; SINCE WE WERE NEXT. THE FO WAS STILL ACCOMPLISHING THE BEFORE TAKEOFF CHKLIST WAITING FOR THE FLT ATTENDANT. THE FLT ATTENDANT WAS CONFIRMING CABIN READY FOR TAKEOFF TO THE FO AND ME; THE FO WAS COMPLETING THE CHKLIST AS WE WERE HOLDING IN POS. AT THIS POINT THE TWR MADE ANOTHER TRANSMISSION TO US. HE CLAIMS; AND I AM TOLD THE TAPES VERIFY; HE ONCE AGAIN CLRED US TO TAXI INTO POS AND HOLD. WHAT I HEARD WAS THAT WE WERE CLRED FOR TAKEOFF. THE FO DIDN'T ACKNOWLEDGE RIGHT AWAY; SO I SAID 'THAT WAS FOR US.' HE ACKNOWLEDGED WITH CALL SIGN; I TURNED ON OUR TAXI LIGHTS AND NOTED A B757 CROSSING IN FRONT OF US ON RWY 4R (LNDG) CLRED AHEAD AND ON FINAL FOR RWY 4R AND 15R; AND TOOK OFF. I SUPPOSE IT IS POSSIBLE I HEARD WHAT I EXPECTED TO HEAR; AND NOT WHAT WAS ACTUALLY SAID BUT; I WOULD TESTIFY WE WERE CLRED TO TAKE OFF IN MY MEMORY. UPON LNDG AT LGA; TWR TOLD US THE TRANSMISSION I HAD THOUGHT WAS TAKEOFF CLRNC WAS ACTUALLY A RESTATEMENT OF A POS AND HOLD CLRNC; ADDING FURTHER THAT TFC WOULD BE TAKING OFF ON RWY 15R. THIS TRANSMISSION WAS NEVER HEARD IN OUR COCKPIT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT THEY WERE FIRST CLRED INTO POS AND HOLD ON RWY 09 PENDING RWY 04R TFC. AFTER TAXIING ONTO THE RWY; THEY WERE AGAIN GIVEN ANOTHER TRANSMISSION TO TAXI POS AND HOLD PENDING TFC ON RWY 15R. BELIEVING THAT THE SECOND TRANSMISSION WAS THEIR TKOF CLRNC; THEY DEPARTED AFTER THE RWY 04R LNDG TFC CLRED THEIR RWY.