I am reading p.3 of Saveliev's Invariants for homology 3-spheres. Here is the construction of a Seifert 3-manifold $X=M(b;(a_1,b_1),\dots,(a_n,b_n))$.
Consider the $S^1$-bundle $M\to S^2$ with Euler number $b\in \Bbb Z$, and let $F=S^2-\operatorname{int}(D^2_1\cup \cdots \cup D^2_n)$ be an $n$-punctured sphere. Over $F$, the bundle $M$ is trivial so $M|_F =F\times S^1$ and $\partial M|_F=\bigcup_{k=1}^n \partial D^2_k\times S^1$ Then paste $n$ solid tori $D^2_k\times S^1$ into $M|_F$ in such a way that the homology class of the meridian of $D^2_k\times S^1$ corresponds to $a_k (\partial D^2_k\times \{1\})+b_k(\{1\}\times S^1)\subset \partial M|_F$. Let $X$ be the resulting Seifert 3-manifold.
Then the book says that $\pi_1(X)$ has presentation $$\langle x_1,\dots,x_n,h~|~h~\text{central}, x^{a_k}h^{b_k}=1, x_1\cdots x_n=h^{-b} \rangle .$$
I can see that $h$ corresponds to the $S^1$ factor of $F\times S^1=M|_F$, and $x_k$ corresponds to the meridian of $\partial D^2_k\times S^1 \subset \partial M|_F$. Then clearly $h$ is central and $x^{a_k}h^{b_k}=1$ from the surgery description. But where does the relation $x_1\cdots x_n=h^{-b}$ come from?