  The paper is concerned with space-time IgA approximations of parabolic
initial-boundary value problems. We deduce guaranteed and fully computable
error bounds adapted to special features of IgA approximations and investigate
their applicability. The derivation method is based on the analysis of
respective integral identities and purely functional arguments. Therefore, the
estimates do not contain mesh-dependent constants and are valid for any
approximation from the admissible (energy) class. In particular, they provide
computable error bounds for norms associated with stabilised space-time IgA
approximations as well as imply efficient error indicators enhancing the
performance of fully adaptive solvers. The last section of the paper contains a
series of numerical examples where approximate solutions are recovered by IgA
techniques. The mesh refinement algorithm is governed by a local error
indicator generated by the error majorant. Numerical results discussed in the
last section illustrate both reliability, as well as the quantitative
efficiency of the error estimates presented.
