it's generally encouraged you replace the flyback along with the new caps. there's a select few tough guys on here that think that's a waste of money or something and that old flybacks don't blow up with new caps. they can, but for the effort you're going to make taking the chassis out to service it, wouldn't it make sense to just do it all right the first time and it continue to work for years?
plus the old flyback anode cups being total trash to handle is, in my opinion, reason enough to replace the flyback.
you may need a new HOT also, with the power obviously off, put meter on diode test, black probe to the monitor frame/copper heatsink wall (not the black one on voltage regulator side, as it's painted and insulated) and touch the red probe to the casing of the HOT. if it reads shorted or the numbers are low, it's bad and you'll need a new one. shorted HOT or bad flyback can blow F901, it's in my experience that fuse won't just blow for its amusement, it means something in the horizontal deflection section is bad.