Knot theory: Braids

Question

Show by using a picture, that the two braids $\sigma_{i} \sigma_{i+1} \sigma_{i}$ and $\sigma_{i+1} \sigma_{i} \sigma_{i+1}$ are equivalent.

This is 5.26 in knot book by Colin Adams. Need some assistance

Answer 1

Here is the drawing of pictures, changing your $\sigma$ to the $T$ below:

You can find this graph anywhere by searching for the braid group or Yang-Baxter equation.