Dual commutative diagrams

Question

I use tikz-cd to draw my commutative diagrams, like the following:

\documentclass{scrartcl}
\usepackage{tikz-cd}
\begin{document}
    \begin{equation}
        \begin{tikzcd}[row sep=scriptsize]
            0 \rar & X \dar["\tilde p", hook, dashed] \rar["x", hook]\ar["\scriptscriptstyle(*)", phantom, dr] & Y \dar["p", two heads]\rar["y", two heads] & Z \dar[equal]\rar & 0\\
            0 \rar & U \rar["u"', hook] & V \rar["v"', two heads] & W \rar & 0
        \end{tikzcd}
    \end{equation}
\end{document}

I want to draw the picture for the dual diagram, which is obtained by the following transformations:

• hooks and double headed tips are exchanged.
• labels of dashed arrows obtain a prime, unless:
• they have a bar or a tilde. In this case, bars and tildes are exchanged.
• $x$- and $y$-coordinates are inverted.

Is it possible to just write down the primal diagram and let TikZ build the dual one automatically?