B737 CREW ON FLT FROM SAL TO MIA REQUESTED A DEV AROUND A VERY LARGE TSTM. THEY WERE TOLD BY THE CTLR THERE WAS NO WX IN THAT LOCATION AND THAT ALL THE PLT WANTED TO DO IS GO DIRECT HIS DEST.

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AT INITIAL HDOF FROM CENAMER CTL TO MERIDA CTR AROUND SATOS INTXN; I WAS PAINTING A MASSIVE TSTM ABOUT 50 MI IN DIAMETER AND TOPS AROUND 40000 FT. I REQUESTED DEV FROM MERIDA CTR AROUND TSTM LOCATED A FEW MI W OF CZM VOR. I ALSO REQUESTED TO FLY DIRECT NUKAN INTXN TO STAY CLR OF ALL WX. MERIDA INFORMED ME THAT THERE WAS NOT A TSTM AT CZM AND THAT I HAD TO REMAIN ON COURSE. I TOLD MERIDA THAT I COULD SEE THE TSTM OVER CZM AND WHEN I REACHED ABOUT 50 MI S OF CZM I WOULD HAVE TO DEV. ABOUT 15 MINS LATER I WAS 50 MI S OF CZM AND AGAIN REQUESTED A HDG OF 050 DEGS FOR DEV AROUND TSTM. MERIDA CTR RESPONDED THAT THERE WAS NOT A TSTM AT CZM AND SAID THAT ALL I WANTED TO DO WAS TO GO DIRECT TO NUKAN. I TOLD HIM THAT IF HE DID NOT GIVE THE HDG TO AVOID THIS TSTM THEN HE WOULD FORCE ME TO DECLARE AN EMER. ALSO; ACR Y AND ACR Z WERE IN THE SAME LOCATION; HEARD THE RADIO CONVERSATIONS; AND ALSO DEVIATED AROUND THE SAME WX SYS. MERIDA DID NOT REALIZE THAT THE TSTM HAD A MASSIVE ANVIL BLOWING OFF THE TOP OF THE TSTM WHICH EXTENDED E OF CZM VOR. I HAVE A COPY OF THE SATELLITE IMAGE WHICH CLRLY SHOWS THIS MASSIVE STORM.