The JSJ-decomposition of the 3-manifold obtained by 0-surgery along a classical pretzel knot of genus one

We consider the JSJ-decomposition of the 3-manifold obtained by 0-surgery along a classical pretzel knot of genus one. We use the classification of exceptional fillings of minimally twisted five-chain links by B. Martelli, C. Petronio and F. Roukema.