A codimension one foliation $\cal F$ on a smooth manifold $M$ is *taut* if every leaf of $\cal F$ meets a closed transversal (i.e., a simple closed curve that is everywhere transversal to the leaves of the foliation). Is it true that a taut foliation admits a closed transversal $\gamma$ that meets *all* leafs of the foliation? 


(I've seen such a curve $\gamma$ being referred to as a total transversal).



taut foliations and the existence of total transversals
Yes, this is true. You can find a proof in Calegari's book, "Foliations and the Geometry of
3–Manifolds", lemma 4.26.


