  In this paper we study the relation between two diagrammatic representations
of links in lens spaces: the disk diagram and the grid diagram and we find how
to pass from one to the other. We also investigate whether the HOMFLY-PT
invariant and the Link Floer Homology are essential invariants, that is, we try
to understand if these invariants are able to distinguish links in $L(p,q)$
covered by the same link in $\mathbf{S}^3$. In order to do so, we generalize
the combinatorial definition of Knot Floer Homology in lens spaces to the case
of links and we analyze how both the invariants change when we switch the
orientation of the link.
