First of all, I want to tell you that using only one \path throughout the picture is not recommended, and you should really use as many \paths as possible if there are different types of lines drawn.
If you want to compress many lines to a single \path, you need something like the edge operation. Unfortunately, edge doesn't accept arc or similar as its option, so I use out and in here. Therefore, the output curves are not exactly the curves in some circles. I hope it is close enough.
I also made some developments to middlearrow style in ferahfeza's nice answer, so that it can handle the nodes.
\documentclass[tikz]{standalone}
\usetikzlibrary{decorations.markings}
\tikzset{
middlearrow/.style n args={3}{
draw,
decoration={
markings,
mark=at position 0.5 with {
\arrow{#1};
\path[#2] node {$#3$};
},
},
postaction=decorate
}
}
\begin{document}
\begin{tikzpicture}[>=stealth]
\coordinate (x) at (0,0);
\coordinate (y) at (0,3);
\path (x) edge[out=60,in=-60,middlearrow={<}{left}{b}] (y)
edge[out=30,in=-30,middlearrow={>}{right}{s}] (y)
edge[out=120,in=-120,middlearrow={<}{right}{a}] (y)
edge[out=150,in=-150,middlearrow={>}{left}{r}] (y);
\end{tikzpicture}
\end{document}

edgeworks very well. Sometimes I use edge to draw some illustrative diagrams when accurate controlling is not necessary. In some cases, I need accurate length and angles of arcs (with middle arrows on them). – Frank Apr 13 '19 at 17:42arcgreater than 90, at least two Bezier curves is used to create the arc. – Frank Apr 13 '19 at 17:42