I've removed a few for friends. This has always worked.
Spray around the threads with a good dose of PB Blaster which is a penetrating oil. Don't use WD-40, it's not a penetrating oil. Let the PB Blaster soak for several hours or overnight. Fill the water heater with water, turn it on and let it get to full temperature for an hour or so. Get a can of compressed air like is used for computer cleaning. Spray the nut of the anode tube, and only the anode tube with the compressed air. Air from an air compressor won't work as it doesn't get cold enough. Air from a can of computer cleaner comes out really cold. What this does is cause a temp difference between the water heater threads and the anode tube, one expanding due to heat and one shrinking due to cold. Using a 6 point socket, extension, and breaker bar you will be able to remove the anode rod unless the threads are severely rusted together. Sometimes you have to tighten the anode rod a bit to break it lose then loosen.
I have yet to have this method fail and I've used it several times for friends.