I have read a statement from Sossinsky and Prasolov' s book "Knots, Lİnks, Braids and 3-Manifold", it says that two reduced word represent isotopic braids if and only if they have the same reduced form, page 54. My claim is that this statement is not true: take $b\_2b\_1b\_2^{-1}b\_3^{-1}b\_3^{-1}$ and $b\_3^{-1}b\_2b\_3b\_2b\_1b\_2^{-1}b\_2^{-1}b\_3^{-1}b\_2^{-1}$. They represent isotopic braids but they are not the same. What is the correct form of such a characterization?