  We study how a gluing construction, which produces compact manifolds with
holonomy G_2 from matching pairs of asymptotically cylindrical G_2-manifolds,
behaves under deformations. We show that the gluing construction defines a
smooth map from a moduli space of gluing data to the moduli space of
torsion-free G_2-structures on the glued manifold, and that this is a local
diffeomorphism. We use this to partially compactify the moduli space of
torsion-free G_2-structures, including it as the interior of a topological
manifold with boundary. The boundary points are equivalence classes of matching
pairs of torsion-free asymptotically cylindrical G_2-structures.
