  We present and analyze a new stable space-time Isogeometric Analysis (IgA)
method for the numerical solution of parabolic evolution equations in fixed and
moving spatial computational domains. The discrete bilinear form is elliptic on
the IgA space with respect to a discrete energy norm. This property together
with a corresponding boundedness property, consistency and approximation
results for the IgA spaces yields an a priori discretization error estimate
with respect to the discrete norm. The theoretical results are confirmed by
several numerical experiments with low- and high-order IgA spaces.
