In the book of "Introduction To Topological Quantum Computation" by Jiannis K. Pachos, in chapter 5, it tries to explain anyonic exchange.
In the following, the $m$ and $e$ quasi-particles are produced by Pauli matrices $σ_x$ and $σ_z$, and the $ϵ$ is made out of their combination.
In the picture below, which is about exchanging two $ϵ$ quasi-particles, I just cannot figure out why the string (or loop) that resulted in the exchange is constructed like the one which comes in the following explanation of the image. Why is it like that? In particular, why is the first parenthesis different from the second one?