In this talk I will explain how considering linear series on a curve X suggests a natural equivalence relation on covers, different from the usual equivalence of covers from the fundamental group. In the usual situation, since the tame fundamental group is finitely generated, there are no families of tame covers of fixed degree and branch locus. However, as first noted by Osserman, under the equivalence suggested by linear series there do exist tame families with fixed degree and ramification locus. In the non-Galois case I will present some results towards classifying when such families can exist. In the Galois case, I will provide a complete classification.