FLC OF A CESSNA CITATION C550 DSNDED WITHOUT CLRNC DURING TRANSITION VECTORS TO AN APCH DUE TO MISUNDERSTANDING THAT THEY HAD CANCELED IFR FOR A VFR DSCNT TO AVOID CLOUDS.

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WE WERE ASSIGNED AN ALT OF 9000 FT AND A HDG OF 340 DEGS AFTER PASSING FMG VOR. AT THE VOR; WE BROKE OUT INTO VMC AND WERE EXPERIENCING MODERATE TURB. I THEN TOLD THE COPLT TO CANCEL IFR SO WE COULD INITIATE A FURTHER DSCNT BEFORE ENTERING MORE CLOUDS AND TURB JUST TO THE N OF OUR POS. I HEARD THE COPLT SAY THAT WE HAD THE ARPT IN SIGHT AND ALSO HEARD THE WORD 'CANCEL' FROM HIM AS WELL. ATC RESPONDED WITH 'ROGER.' WE THEN PROCEEDED TO DSND WHILE MAINTAINING THE 340 DEG HDG. WE WERE WAITING FOR FURTHER INSTRUCTIONS FROM ATC WHEN WE RECEIVED A QUERY AS TO OUR ALT. AFTER STATING OUR ALT; ATC GAVE US AN ALT ASSIGNMENT OF 7200 FT AND A HDG OF 270 DEGS. I THEN TOLD THE COPLT TO VERIFY THAT ATC HAD RECEIVED OUR IFR CANCELLATION. RATHER THAN VERIFYING; THE COPLT RE-CANCELLED THE IFR CLRNC. WE RECEIVED OUR LNDG INSTRUCTIONS AND PROCEEDED TO THE ARPT. THE CTLR INFORMED US THAT WE INITIATED A PLTDEV. I THEN COMMUNICATED THAT HE ACKNOWLEDGED OUR CANCELLATION BY STATING 'ROGER.' ONCE ON THE GND; I CALLED THE TWR SUPVR AND FOUND THAT THEY HAD NOT HEARD US CANCEL IFR. HEARING THE WORD 'ROGER' TO ME MEANT THAT HE RECEIVED OUR IFR CANCELLATION. IF HE HAD SAID 'ROGER; EXPECT THE VISUAL TO RWY 16L;' I WOULD HAVE KNOWN RIGHT AWAY THAT HE DIDN'T RECEIVE OUR FULL MESSAGE. I DO KNOW NOW THAT I SHOULD ONLY ACCEPT THE WORDS 'CANCELLATION RECEIVED' BEFORE INITIATING VFR FLT RULES. AFTER DISCUSSING THE COMS PROB WITH THE COPLT; HE THOUGHT THAT HE MAY HAVE UNKEYED THE MIKE DURING SOME OF THE TURB; THUS NOT XMITTING OUR FULL MESSAGE TO ATC.