Genericity of pseudo-Anosov mapping classes, when seen as mapping classes

We prove that any mapping torus of a pseudo-Anosov class with bounded normalized Weil-Petersson translation length contains finite set transverse and level closed curves, drilling out this curves results in one number cusped hyperbolic 3-manifolds. The manifolds the list depends only on bound for length. also complementary result explains necessity removing by producing new estimates compositions classes arbitrary powers Dehn twist.