Hi,
In this case I think compatible can be defined as producing a visually distinct animal with only one gene from each line. Thats not really a correct explanation though - just the simplest way of thinking about it I can come up with.
If the OP has a VPI line axanthic het and buys another het axanthic that turns out to be from the snake keeper line then breeding them together will never give him a visually axanthic animal but instead give him a clutch of "33% possible double hets".
Breeding the possible double hets together could give him visuals of both types of axanthic, an animal what visually expressed both lines of axanthic (not sure how that would look) and normal looking animals.
Genetically the normals would be "possible double hets", the single line visuals would be poss hets for the other line and the only animal whos genetics wouldn't be in doubt without further breeding would be the double homozygous dual line animal. ( I tried to work out the percentages but had a brain fart so gave up ).
Er... I think.
It could take him 6 - 10 years or more to feel confident that he knew the genetics of each animal from the first and second clutches. And even then he might never be certain.
This is why everyone is stressing the problem with buying anything aside from a visual axanthic to pair with his original het axanthic - if he did end uo with different lines then he could at least say the result of the breding was 100% het for the line the visual parent came from.
Now did that help or have I confused you as much as I have myself?
dr del