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I do not know how to appropriately describes this kind of feature in beamer.

I'm watching some presentations on youtube and I'm interested in how this presenter is transitioning the figure in this presentation that makes room for the text to appear: https://youtu.be/qEAIJXxd0nQ?t=12m20s

I know you can make unique slide transitions in beamer, but how is one able to smoothly move figures as an animation to the side of the same slide?

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With slide transitions one could create a similar effect:

\documentclass{beamer}

\begin{document}

\begin{frame}
\transwipe<1-3>[direction=0]

\begin{onlyenv}<1>
    \begin{figure}
        \includegraphics[width=.7\textwidth]{example-image}
    \end{figure}
\end{onlyenv}

\begin{onlyenv}<2->
    \begin{columns}[onlytextwidth]
        \begin{column}{.7\textwidth}
            \centering  
            \includegraphics[width=\textwidth]{example-image}
        \end{column}
        \begin{column}<3->{.25\textwidth}
            text text text text text
        \end{column}
    \end{columns}
\end{onlyenv}

\end{frame} 

\end{document}
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