  In this paper we study skeleta of residually tame coverings of a marked curve
over a non-archimedean field. We first generalize a result by Liu and Lorenzini
by proving a simultaneous semistable reduction theorem for residually tame
coverings. We then use this to construct a functor from the category of
residually tame coverings of a marked curve $(X,D)$ to the category of tame
coverings of a metrized complex $\Sigma$ associated to $(X,D)$. We enhance the
latter category by adding a set of gluing data to every covering and we show
that this yields an equivalence of categories. Using this equivalence, we then
define filtrations of the fundamental group of the marked curve, giving for
instance the absolute decomposition and inertia groups of the metrized complex.
We then use the analytic slope formula to prove that the extensions that arise
from the abelianizations of the decomposition and inertia quotients coincide
with the extensions that arise from the toric and connected parts of the
analytic Jacobian of the curve.
