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My appendices are rather small and I want them to come one after another (like \section) without the blank page before \chapter{} (due to openright option). Another problem is that chapter headings take a lot of vertical space above and below them.

How can we remove or decrease these spaces? so that \chapter behaves almost like \section.

Take a look:

\documentclass[11pt,a4paper,twoside,openright]{book}
...
\begin{appendices}
\appendixpage
\noappendicestocpagenum
\addappheadtotoc

\chapter{}
\begin{table}
\centering
\caption{Reservoir relative permeability chart ($k_r$ vs. $S_w$).}
\begin{tabular}{c}
...

Take a look: Output http://8pic.ir/images/25061788036600309756.png

I wish I was clear.

1

You can control the space with \renewcommand{\chapterheadstartvskip}{\vspace*{-\baselineskip}} to be like \section.

I don't know about the open<?> option of the book class, but with KOMAscript you can change that option later on:

\documentclass[open=right]{scrbook}
\usepackage{lipsum}
\renewcommand{\chapterheadstartvskip}{\vspace*{-\baselineskip}}
\begin{document}
\mainmatter
\chapter{Eins}
\lipsum[1-5]
\chapter{Zwei}
\lipsum[6-10]

\backmatter\KOMAoptions{open=any}
\chapter{Uno}
\lipsum[11-15]
\chapter{Due}
\lipsum[16-20]
\end{document}

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