I think there may be some newer Axanthic lines that are just different lines but the original VPI, TSK, and Jolliff lines appear to be different genes all together. They are just all called axanthics based on what the animal looks like but I think it would be more accurate to call them different mutations that different lines.
While I do agree on those (and several others - Vin Russo, special, and hidden) appearing to be the same gene I don't think that gene moves at all (right?). I think they are just each mutated in slightly different ways. I'm not sure exactly how the start and end of a gene is defined but within the gene I believe there is a quite a bit of information and it looks like multiple different mistakes have happen to this particular gene.