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The only thing that's 'true' is if your CPU is both supported by the Socket and the BIOS {CPUID}. Further, the reason for AM2+ to AM3 is for DDR3, and doesn't support the AM2/AM2+ CPU. See below.
So what exact 'AMD' Anton 64 X2 do you have now?
"AM3 processor + AM2 motherboard with DDR2 slots = works
AM3 processor + AM3 motherboard with DDR3 and DDR2 slots = works with either of the memory types
AM2/AM2+ processor + AM3 motherboard with DDR3 and DDR2 slots = works with the DDR2 slots
AM2/AM2+ processor + AM3 motherboard with DDR3 slots = will not work."