\documentclass[tikz]{standalone}

\usetikzlibrary{decorations.pathreplacing,decorations.markings}
\usetikzlibrary{patterns}
\begin{document}

\begin{tikzpicture}
%%%% ordinary arc +1 definition
% draw exterior arcs
\draw (0,1) to (1,0);
\draw (1,0) to (2,1);
\draw (2,1) to (1,2);
\draw (1,2) to (0,1);
\draw (1,0) to (1,2);

%draw vertices
\draw[fill=black] (0,1) circle[radius=2pt];
\draw[fill=black] (1,0) circle[radius=2pt];
\draw[fill=black] (1,2) circle[radius=2pt];
\draw[fill=black] (2,1) circle[radius=2pt];

%draw lamination
\draw[out=30,in=-120,red,densely dashed] (0.3,0.3) to (1.7,1.7);

%label
\node[scale=1,red] at (1,-0.5) {$+1$};

%%%% ordinary arc -1 definition
% draw exterior arcs
\draw (3,1) to (4,0);
\draw (4,0) to (5,1);
\draw (5,1) to (4,2);
\draw (4,2) to (3,1);
\draw (4,0) to (4,2);

%draw vertices
\draw[fill=black] (3,1) circle[radius=2pt];
\draw[fill=black] (4,0) circle[radius=2pt];
\draw[fill=black] (4,2) circle[radius=2pt];
\draw[fill=black] (5,1) circle[radius=2pt];

%draw lamination
\draw[out=-60,in=160,red,densely dashed] (3.3,1.7) to (4.7,0.3);

%label
\node[scale=1,red] at (4,-0.5) {$-1$};

%%%% pending arc +1 definition
%draw exterior boundaries
\draw[out=30,in=-30,looseness=1.5] (7,0) to (7,2);
\draw[out=150,in=-150,looseness=1.5] (7,0) to (7,2);

%add pending arc
\draw[in=0,out=45,looseness =1.25] (7,0) to (7,1.7);
\draw[in=180,out=135,looseness=1.25] (7,0) to (7,1.7);

%lamination
\draw[in=0,out=30,looseness =1.25, densely dashed, red] (6.8,0) to (7,1.5);
\draw[in=180,out=115,looseness=1.25, densely dashed, red] (6.8,0) to (7,1.5);

%draw vertices and orbifold point
\draw[fill=black] (7,0) circle [radius=2pt];
\draw[fill=black] (7,2) circle [radius=2pt];
\draw[thick] (7,1.3) node {$\mathbf{\times}$};

%label
\node[scale=1,red] at (7,-0.5) {$+1$};

%%%% pending arc -1 definition
%draw exterior boundaries
\draw[out=30,in=-30,looseness=1.5] (9.5,0) to (9.5,2);
\draw[out=150,in=-150,looseness=1.5] (9.5,0) to (9.5,2);

%add pending arc
\draw[in=0,out=45,looseness =1.25] (9.5,0) to (9.5,1.7);
\draw[in=180,out=135,looseness=1.25] (9.5,0) to (9.5,1.7);

%lamination
\draw[out=-40, in = 0, red,densely dashed,looseness=0.75] (9.8,2) to (9.5,0.8);
\draw[out=180, in = -160, red,densely dashed] (9.5,0.8) to (9.8,2);

%draw vertices and orbifold point
\draw[fill=black] (9.5,0) circle [radius=2pt];
\draw[fill=black] (9.5,2) circle [radius=2pt];
\draw[thick] (9.5,1.3) node {$\mathbf{\times}$};

%label
\node[scale=1,red] at (9.5,-0.5) {$-1$};

\end{tikzpicture}

\end{document}