\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{arrows}

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[thick]
%\node (name) at position {lable}; 
\node (00) at (0,0) {$0$};
\node (20) at (2,0) {$A^\prime$};
\node (40) at (4,0) {$B^\prime$};
\node (60) at (6,0) {$C^\prime$};
\node (80) at (8,0) {$0$};

\node (02) at (0,2) {$0$};
\node (22) at (2,2) {$A$};
\node (42) at (4,2) {$B$};
\node (62) at (6,2) {$C$};
\node (82) at (8,2) {$0$};

\draw[->] (00) -- (20);
\draw[->] (20) -- (40);
\draw[->] (40) -- (60);
\draw[->] (60) -- (80);

\draw[->] (02) -- (22);
\draw[->] (22) -- (42);
\draw[->] (42) -- (62);
\draw[->] (62) -- (82);

\draw[double distance=2pt] (20) --(22);
\draw[<-] (40) -- node [left] {$\approx$} (42); 
\draw[double distance=2pt] (60) -- (62);
\end{tikzpicture}
\end{document}