  In this short note, we give an explicit construction of inequivalent
Lefschetz pencils and fibrations of same genera on blow-ups of all rational and
ruled surfaces. This complements our earlier results, concluding that every
symplectic 4-manifold, after sufficiently many blow-ups, admits inequivalent
Lefschetz pencils and fibrations, which cannot be obtained from one another
even via any sequence of fibered Luttinger surgeries.
