Pensieve header: MVA1 agrees with MVA2, and MVA2 is an excellent normalization for MultivariableAlexander!

<< KnotTheory`

MV1= (MultivariableAlexander[#, Program -> "MVA1"]&);
MV2= (MultivariableAlexander[#, Program -> "MVA2"]&);

test1[L_] := (
mv=MV1[L][t]; mv2=First[MV2[L][t]];
Or @@ Map[
(mv1=mv /. t[i_] :> t[#[[i]]]; Head[Expand[Simplify[mv2/mv1]]]=!=Plus)&,
Permutations[Range[Length[Skeleton[L]]]]
]
);
Print[# ->test1[#]]& /@ AllLinks[9];

{MV1[Link[9,NonAlternating,27]][t], MV2[Link[9,NonAlternating,27]][t]}

Flip[X[i_,j_,k_,l_]] := If[l==j+1 || j-l>1, X[j,k,l,i], X[l,i,j,k]];
VCube[pd_, l_List] := Module[
{f},
Expand[pd*Times @@ ((1-f[#])& /@ l)] //. pd1_PD*f[i_] :> MapAt[Flip, pd1, i]
]

Series[VCube[PD[#], {1,2, 7}] /. pd_PD :> Jones[pd][E^x], {x, 0,3}]& /@AllLinks[8]

Print[# -> Series[VCube[PD[#], {1,2, 7}] /. pd_PD :> MV2[pd][t] /. t[i_] -> E^(h x[i]), {h, 0, 2}]]& /@AllLinks[8];

Print[# -> Series[VCube[PD[#], {1,2, 7}] /. pd_PD :> MV2[pd][t] /. t[i_] -> E^(h x[i]), {h, 0,2}]]& /@AllLinks[9];

Print[# -> Series[VCube[PD[#], {1,2, 7,8}] /. pd_PD :> MV2[pd][t] /. t[i_] -> E^(h x[i]), {h, 0,2}]]& /@AllLinks[9];

Print[# -> Series[VCube[PD[#], {1,2,5, 7,9}] /. pd_PD :> MV2[pd][t] /. t[i_] -> E^(h x[i]), {h, 0, 3}]]& /@AllLinks[11];