\documentclass{article}

\usepackage{amsmath}

\begin{document}

\begin{align*}
  1 + 2
\end{align*}
\begin{align*}
  3 + 4
\end{align*}

\setlength{\abovedisplayskip}{0pt}
\setlength{\abovedisplayshortskip}{0pt}
\setlength{\belowdisplayskip}{0pt}
\setlength{\belowdisplayshortskip}{0pt}

\begin{align*}
  1 + 2
\end{align*}
\begin{align*}
  3 + 4
\end{align*}

\end{document}