Building further on work of Marin and Wagner, we give a cubic braid-type skein theory of the Links--Gould polynomial invariant of oriented links and prove that it can be used to evaluate any oriented link, adding this polynomial to the list of polynomial invariants that can be computed by skein theory. As a consequence, we prove that this skein theory is also shared by the V₁-polynomial defined by two of the authors, deducing the equality of the two link polynomials. This implies specialization properties of the V₁-polynomial to the Alexander polynomial and to the ADO₃-invariant, the fact that it is a Vassiliev power series invariant, as well as a Seifert genus bound for knots.
Garoufalidis et al. (Sun,) studied this question.