  We present and analyze a stable space-time multi-patch discontinuous Galerkin
Isogeometric Analysis (dG-IgA) scheme for the numerical solution of parabolic
evolution equations in moving space-time computational domains. Following
\cite{LangerMooreNeumueller:2016a}, we use a time-upwind test function and
apply multi-patch discontinuous Galerkin IgA methodology for discretizing the
evolution problem both in space and in time. This yields a discrete bilinear
form which is elliptic on the IgA space with respect to a space-time dG norm.
This property together with a corresponding boundedness property, consistency
and approximation results for the IgA spaces yields an \textit{a priori
discretization} error estimate with respect to the space-time dG norm. The
theoretical results are confirmed by several numerical experiments with low-
and high-order IgA spaces.
