Let $ \Phi $ be a $C^2$ codimension one Anosov flow on a compactRiemannian manifold $M$ of dimension greater than three. Verjovskyconjectured that $ \Phi $ admits a global cross-section and we affirmthis conjecture when $ \Phi $ is volume preserving in the followingtwo cases: (1) if the sum of the strong stable and strongunstable bundle of $\Phi$ is $ \theta $-Hölder continuous for all $\theta < 1 $; (2) if the center stable bundle of $ \Phi $ isof class $ C^{1 + \theta} $ for all $ \theta < 1 $. We also show howcertain transitive Anosov flows (those whose center stable bundle is$C^1$ and transversely orientable) can be ‘synchronized’, thatis,reparametrized so that the strong unstable determinant of the time $t$map (for all $t$) of the synchronized flow is identically equal to $e^t $. Several applications of this method are given, includingvanishing of the Godbillon–Vey class of the center stable foliation ofa codimension one Anosov flow (when $ \dim M > 3 $ and that foliationis $ C^{1 + \theta} $ for all $ \theta < 1 $), and a positive answerto a higher-dimensional analog to Problem 10.4 posed by Hurder andKatok in [HK].