Diagramme

\documentclass[11pt]{beamer}
\usetheme{Warsaw}
\usepackage[utf8]{inputenc}

\begin{document}
\begin{frame}{A diagram}
\begin{equation*}
\begin{array}{c c c}
\fbox{my text in a box}
& \longleftrightarrow
& 
\left\{
    \begin{array}{ll}
        x &= f(y+z) \\
        y &= g(x)
    \end{array}\right.

\\  
&
& \displaystyle\left\Updownarrow\vphantom{\int}\right.
\\ 
& 
&  
\left\{
    \begin{array}{ll}
    x &= f(y+z) \\
    y &= g(x)
    \end{array}
\right.
\end{array}
\end{equation*}
\end{frame}
\end{document}