  We introduce a framework to analyze knots and links in an unmarked solid
torus. We discuss invariants that detect when such links are equivalent under
an ambient homeomorphism, and show that the multivariable Alexander polynomial
is such in invariant. We compute, for links with low wrapping number, bounds on
the degree of a Dehn twist needed to transform one into the other that depend
on the dichromatic Kauffman polynomial. Finally, we use this to give a
classification of all non-split links up to 6 crossings in the unmarked solid
torus.
