Big vertices on my cube kill parallelism

With help of calc package, make a box of width B with left alignment and put B\cup_A C inside. Do the same for B'\cup_{A'}C'. Here these two quantities protrude to the right, but I hope that is OK.

\documentclass{article}
\usepackage{xypic,calc}
\begin{document}
  \[
  \xymatrix{
& B \ar[rr] \ar'[d][dd]^(.45)\simeq && \makebox[\widthof{$B$}][l]{$B\cup_A C$} \ar@{.>}[dd]^-\simeq \\
A \ar@{>->}[ru] \ar[rr] \ar[dd]_-\simeq && C \ar@{>->}[ru] \ar[dd]^(.68)\simeq & \\
& B' \ar'[r][rr] && \makebox[\widthof{$B$}][l]{$B'\cup_{A'}C'$} \\ A' \ar@{>->}[ru] \ar[rr] && C' \ar@{>->}[ru] &
}
\]
\end{document}