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I need some advice on removing the bearings in the sprocket carrier.

Depends on wether your wanting to fit new bearings or refit the old ones . If your fitting new you could just drive the old ones out with a punch and discard . If you want to re-use then you need to be a bit more careful and use either a bearing puller or a press .
If you heat the carrier with some sort if flame thrower...concentrating flame on the carrier rather than the bearing they might just fall out as the carrier expands . And this is probly the easiest way to fit new ...just heat the carrier and the new bearings will just slide in . Doesnt need to be stupid hot ...somewhere around 100⁰c is usually enough

Success! Thanks for the advice. It was the inner race that was fooling me. A little heat, a vice, a socket, and a BFH and out they all pop!

Cool . Be aware that sprocket bolts are well known to come loose and carve a chunk out of your swing arm . You may think you'd notice as soon as a bolt makes contact but apparently not , seems peeps usually dont and ride along oblivious to the carnage going on untill they are stopped and actually see the damage. Employ whatever your favorite bolt /nut locking method is ....loctite ,lock nuts ( use once only ....they aint that expensive )and good spring washers , I dont think you need to lock wire them but it cant hurt ....specially if you have the ability to do it .