How to avoid a jumpy slide while using \only?

All you need to do is to at t to the options of the frame.

\documentclass[10pt,english,xcolor={usenames,dvipsnames}]{beamer}
\begin{document}


\begin{frame}[label=id1,t]
\frametitle{A non-identification result}
\begin{itemize}
\item<1-> 1
\begin{itemize}
\item<2->   The equation is
    \only<2>{\begin{equation*}
    x = y
        \end{equation*}}
    \only<3>{\begin{equation*}x = z
    \end{equation*}}
    \onslide<4->{\begin{equation*}x=\textcolor{red}{z}
    \end{equation*}} 
    \item<4-> yet \\ 
     \onslide<5->...  $x = u$
\end{itemize}
\item<6-> There is a jump at 2
\item<7-> and at 4
\end{itemize}
\end{frame}
\end{document}

Some (2) tricks as ideas to use in such cases:

\documentclass[10pt,english,xcolor={usenames,dvipsnames}]{beamer}
\begin{document}


\begin{frame}[label=id1]
\frametitle{A non-identification result}
\begin{itemize}
\item<1-> 1
\begin{itemize}
\item<2->   The equation is
    \onslide<2->{\begin{equation*}
   \alt<2>{x=y}{x=\textcolor{red}{z}}
    \end{equation*}}
    \only<1-3>{\invisible<1-3>{\item .\\}}
    \only<4->{\item<4->yet \\}
     \onslide<5->...  $x = u$
\end{itemize}
\item<6-> There is not a jump at 2
\item<7-> neither at 4
\end{itemize}
\end{frame}
\end{document}