\documentclass[tikz]{standalone}

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

\begin{document}

\begin{tikzpicture}

% sets up command for arrows in the middle of arcs
\tikzset{->-/.style={decoration={
  markings,
  mark=at position #1 with {\arrow{>}}},postaction={decorate}}}


%exterior edges
\draw[out=30,in=-30,looseness=1.5] (0,0) to (0,1.5);
\draw[out=150,in=-150,looseness=1.5] (0,0) to (0,1.5);

%add labels
\node[left,xshift=1pt,scale=0.6] at (-0.5,1.1) {$\alpha$};
\node [right,xshift=-1pt,scale=0.6] at (0.5,1.1) {$\beta$};
\node [above below,xshift=-1pt,scale=0.6] at (0.2,0.4) {$\rho$};

%pending arc edges
\draw[in=0,out=45,looseness =1.25] (0,0) to (0,1.3);
\draw[in=180,out=135,looseness=1.25] (0,0) to (0,1.3);

%draw crossing arc
\draw[orange, thick,out=100,in=180,looseness = 1.25] (0,0) to (0,1.25);
\draw[orange, thick,out=0,in=0,looseness = 1] (0,1.25) to (0.05,0.78);
\draw[orange, thick,out=180,in=-90,looseness = 1] (0.05,0.78) to (-0.1,1.1);
\draw[orange, thick,out=90,in=0,looseness = 3] (-0.1,1.1) to (0,0.85);
\draw[orange, thick,out=180,in=275,looseness = 1] (0,0.85) to (-0.3,1.3);

%draw vertices and orbifold point
\draw[fill=black] (0,0) circle [radius=2pt];
\draw[fill=black] (0,1.5) circle [radius=2pt];
\draw[thick] (0,1) node {$\mathbf{\times}$};

\end{tikzpicture}

\end{document}