Not an answer, just too long for a comment. This shows how to use standalone class with pdflatex.
\documentclass{standalone}
%\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{tikz-cd}
\usepackage{mathtools, amssymb}
% \usepackage{pst-node, auto-pst-pdf}% ???
\begin{document}
\begin{tikzcd}[sep=large]
M \rar \dar["\mathrm{Pinch}" ' ] \arrow[dr, dashed, "\beta_1 + \beta_2 + \beta_3 = 0", sloped] & * \rar \dar & \Sigma M \dar \rar & \Sigma M \dar \\%
M \vee M \vee M \rar[swap, "{(\beta_1 , \beta_2 , \beta_3)}" ] & N \rar & N' \rar & \Sigma M \vee \Sigma M \vee \Sigma M \rar[swap, "{(\beta_1 , \beta_2 , \beta_3)}" ] & N \rar & N' \rar & \Sigma M \vee \Sigma M \vee \Sigma M
\end{tikzcd}
\end{document}

This is how to produce the same diagram (more of less) using a plain tikzpicture.
\documentclass{standalone}
%\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{mathtools, amssymb}
\usepackage{tikz}
\usetikzlibrary{matrix,arrows.meta,calc}
\begin{document}
\begin{tikzpicture}
\matrix (A) [matrix of math nodes, row sep=2cm, column sep={3cm,between origins}]{
M & * & \Sigma M & \Sigma M \\
M \vee M \vee M & N & N' & \Sigma M \vee \Sigma M \vee \Sigma M \\
N & N' & \Sigma M \vee \Sigma M \vee \Sigma M \\
};
\draw[->] (A-1-1) -- (A-1-2);
\draw[->] (A-1-2) -- (A-1-3);
\draw[->] (A-1-3) -- (A-1-4);
\draw[->] (A-1-1) -- (A-2-1) node[midway,left] {Pinch};
\draw[->] (A-1-2) -- (A-2-2);
\draw[->] (A-1-3) -- (A-2-3);
\draw[->] (A-1-4) -- (A-2-4);
\draw[dashed,->] (A-1-1) -- (A-2-2) node[midway,above,sloped] {$\beta_1 + \beta_2 + \beta_3 = 0$};
\draw[->] (A-2-1) -- (A-2-2) node[midway,below] {$(\beta_1 , \beta_2 , \beta_3)$};
\draw[->] (A-2-2) -- (A-2-3);
\draw[->] (A-2-3) -- (A-2-4);
\draw[thick,green,->] (A-2-4) |- ($(A-2-4)!0.5!(A-3-1)$)% midway
node[below, black]{$(\beta_1 , \beta_2 , \beta_3)$}
-| (A-3-1);
\draw[->] (A-3-1) -- (A-3-2);
\draw[->] (A-3-2) -- (A-3-3);
\end{tikzpicture}
\end{document}
