node[empty,name=s3t] {} 
(0.5,2.7) node[empty,name=s2t] {} 
(0,2.7) node[empty,name=s1t] {} 
(-0.5,-0.5) node[empty,name=s1b] {} 
(0.0,-0.5) node[empty,name=s2b] {} 
(1,-0.5) node[empty,name=s3b] {} 
(-0.5,2.7) node[empty,name=s0t] {};
\draw[braid] (s3t) to[out=315,in=45] (t1u);
\draw[braid] (s2t) to[out=270,in=135] (t1u);
\draw[braid] (t1u) to[out=315,in=45] (t1d);
\draw[braid] (t1d) to[out=300,in=80] (s3b);
\draw[braid] (s0t) to[out=225,in=135] (t2);
\draw[braid] (s1t) to[out=315,in=45] (t2);
\draw[braid] (t2) to[out=260,in=100] (s1b);
\path[braid,name path=s4] (t2) to[out=315,in=135] (t1d);
\path[braid,name path=s6] (t1d) to[out=210,in=180] (m);
\draw[braid,name path=s5] (t1u) to[out=225,in=0] (m);
\fill[white, name intersections={of=s4 and s5}] (intersection-1) circle(0.1);
\fill[white, name intersections={of=s6 and s5}] (intersection-1) circle(0.1);
\draw[braid] (t2) to[out=315,in=135] (t1d);
\draw[braid] (t1d) to[out=210,in=180] (m);
\draw[braid] (m) to (s2b);
\draw (1.6,1.35) node {$\stackrel{(a)}=$};
\end{tikzpicture}
\begin{tikzpicture}
    \path (0.75,1.0) node[arr,name=t1] {$t_1$} 
(0.5,1.5) node[arr,name=m]  {} 
(-0.25,2) node[arr,name=t2] {$t_2$}; 
\path (1.0,2.7) node[empty,name=s3t] {} 
(0.5,2.7) node[empty,name=s2t] {} 
(0,2.7) node[empty,name=s1t] {} 
(-0.5,-0.5) node[empty,name=s1b] {} 
(0.0,-0.5) node[empty,name=s2b] {} 
(1,-0.5) node[empty,name=s3b] {} 
(-0.5,2.7) node[empty,name=s0t] {};
\draw[braid] (s3t) to[out=270,in=45] (t1);
\draw[braid] (s2t) to[out=270,in=0] (m) to[out=180,in=315] (t2);
\draw[braid] (s0t) to[out=225,in=135] (t2);
\draw[braid] (s1t) to[out=315,in=45] (t2);
\draw[braid] (t2) to[out=260,in=100] (s1b);
\draw[braid] (m) to[out=270,in=135] (t1);
\draw[braid] (t1) to[out=225,in=90]  (s2b);
\draw[braid] (t1) to[out=280,in=80] (s3b);
\draw (1.6,1.35) node {$\stackrel{\eqref{eq:m_t_1-2}}=$};
\end{tikzpicture}
\begin{tikzpicture}
    \path (0.75,1.0) node[arr,name=t1d] {$t_1$} 
(0.25,2) node[arr,name=t1u] {$t_1$}
(-0.25,0.5) node[arr,name=m]  {} ;
\path (1.0,2.7) node[empty,name=s3t] {} 
(0.5,2.7) node[empty,name=s2t] {} 
(0,2.7) node[empty,name=s1t] {} 
(-0.25,-0.5) node[empty,name=s1b] {} 
(0.5,-0.5) node[empty,name=s2b] {} 
(1,-0.5) node[empty,name=s3b] {} 
(-0.5,2.7) node[empty,name=s0t] {};
