\documentclass[12pt]{article}
\usepackage{amsthm,amssymb,amsmath}
\usepackage{pgf,pgfplots,tikz}
%\pgfplotsset{width=7cm,compat=newest}
\usetikzlibrary{snakes,arrows,matrix,shapes,backgrounds}
\begin{document}
\section{1}
$$
\begin{tikzpicture}[thick,>=stealth,->,shorten >=2pt,looseness=.5,auto,descr/.style={fill=white}]
\matrix [matrix of math nodes,row sep=10mm,column sep=10mm]
{
&|(1)|\mathcal{U}_\alpha& \\
|(2)|\Sigma_g &  &|(3)|\mathcal{U}_\alpha \cup_\Sigma \mathcal{U}_\beta\\
&|(4)|\mathcal{U}_ \beta&\\
};
\begin{scope}[every
node/.style={->,sloped,midway,auto,font=\scriptsize}]
\draw (2) -- node[] {$i^\alpha$} (1);
\draw (2) -- node[] {$i^\beta$} (4);
\draw (1) -- node[] {$I^\alpha$} (3);
\draw (4) -- node[] {$I^\beta$} (3);
\end{scope}
\end{tikzpicture}
$$
\end{document}