= Solution
Two explicit fibrations of $L(2,1)=\mathbb{RP}^3$ are supplied by <Seifert fibrations of real projective 3-space>:
* The ordinary <Hopf fibration> descends from $S^3$ to a circle bundle over $S^2$ with \b[zero exceptional fibers].
* The weighted circle action induced by $(z_1,z_2)\mapsto(e^{it}z_1,e^{3it}z_2)$ has quotient orbifold $S^2$ and \b[one exceptional fiber of multiplicity three].
Thus these are Seifert fibered descriptions of the same filled manifold with different numbers of exceptional fibers.
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