Side by side pages synchronised by heading

Question

Apologies if the question title is not clear, feel free to edit or provide suggestions.

Currently I am typing up my maths notes and my system is to have definitions on the left page and proofs on the right page. Below is an example of what I'm doing where I've used an A3 page and two minipages.

While I can be a bit creative with printing to "convert" it to A4 pages, the result isn't great (dead hyperlinks, etc). I've tried writing my own macros and class, but I can't work out how to get the correct vertical spacing on the right page to match the spacing on the left page and vice versa such that the left and right pages are synchronised by heading.

Any help or pointers would be much appreciated as I couldn't find anything when I searched stackexchange.

\documentclass[12pt, landscape]{book}

\usepackage{lipsum}
\usepackage{geometry}
\geometry{a3paper, tmargin=1in, bmargin=1in, lmargin=1in, rmargin=1in}

\begin{document}
\setcounter{chapter}{1}
\section{Some Topic}
    \begin{minipage}[t]{0.48\textwidth}
    \lipsum[1]
    \end{minipage}
    \hfill\vline\hfill
    \begin{minipage}[t]{0.48\textwidth}
    \lipsum[2-3]
    \end{minipage}
\section{Another Topic}
    \begin{minipage}[t]{0.48\textwidth}
    \lipsum[4]
    \end{minipage}
    \hfill\vline\hfill
    \begin{minipage}[t]{0.48\textwidth}
    \lipsum[5-6]
    \end{minipage}
\end{document}

Answer 1

You can use the paracol package (1 column per page over 2 pages).

\documentclass[12pt]{book}

\usepackage{lipsum}
\usepackage{paracol}

\begin{document}
\begin{paracol}[1]{2}
\setcounter{chapter}{1}
  \switchcolumn[0]*[\section{Some Topic}]
    \lipsum[1]
  \switchcolumn[1]
    \lipsum[2-3]
\switchcolumn[0]*[\section{Another Topic}]
    \lipsum[4]
    \switchcolumn[1]
    \lipsum[5-6]
\end{paracol}
\end{document}