  We study the boundary behavior of solutions to parabolic double-phase
equations through the celebrated Wiener's sufficiency criterion. The analysis
is conducted for cylindrical domains and the regularity up to the lateral
boundary is shown in terms of either its $p$ or $q$ capacity, depending on
whether the phase vanishes at the boundary or not. Eventually we obtain a fine
boundary estimate that, when considering uniform geometric conditions as
density or fatness, leads us to the boundary H\"older continuity of solutions.
In particular, the double-phase elicits new questions on the definition of an
adapted capacity.
