\documentclass[11pt,leqno]{amsart}

%\usepackage{amsthm}

\newcommand{\pathtotrunk}{./}

\input{text/article_preamble}

\input{text/top_matter}

\input{text/kw_macros}

%\title{Blob Homology}

\title{Sandbox}

\begin{document}

\begin{equation*}

\begin{tikzpicture}

\def\rad{1}

\def\srad{0.75}

\foreach \i in {0, 1, 2} {

	\node(\i) at ($\i*(4.5,0)$) {};

}

\draw (0) circle (\rad);

\draw ($(1)+(1,0)$) circle (\srad);

\draw[fill=white] (1) circle (\rad);

\begin{scope}

\draw[clip] (2) circle (\rad);

\draw ($(2)+(1,0)$) circle (\srad);

\end{scope}

\end{tikzpicture}

\end{equation*}

\begin{equation*}

\begin{tikzpicture}

\node(M) at (0,0) {$M$};

\foreach \angle/\label in {0/K', 45/K'L, 90/L, 135/KL, 180/K, 225/KL', 270/L', 315/K'L'} {

	\node(\label) at (\angle:4) {$\label$};

}

\foreach \label in {K', L, K, L'} {

	\node(\label M) at ($(M)!0.6!(\label)$) {$\label M$};

	\draw[->] (\label M)--(M);

	\draw[->] (\label M)--(\label);

}

\foreach \k in {K, K'} {

	\foreach \l in {L, L'} {

		\node(\k \l M) at (intersection cs: first line={(\k M)--(\l)}, second line={(\l M)--(\k)}) {$\k \l M$};

		\draw[->] (\k \l M)--(M);

		\draw[->] (\k \l M)--(\k \l );

		\draw[->] (\k \l M)--(\k M);

		\draw[->] (\k \l M)--(\l);

		\draw[->] (\k \l M)--(\l M);

		\draw[->] (\k \l M)--(\k);

	}

}

\draw[->] (K'L') to[bend right=10] (K');

\draw[->] (K'L') to[bend left=10] (L');

\draw[->] (KL') to[bend left=10] (K);

\draw[->] (KL') to[bend right=10] (L');

\draw[->] (K'L) to[bend left=10] (K');

\draw[->] (K'L) to[bend right=10] (L);

\draw[->] (KL) to[bend right=10] (K);

\draw[->] (KL) to[bend left=10] (L);

\end{tikzpicture}

\end{equation*}

\end{document}