  For some geometries including symplectic and contact structures on an
n-dimensional manifold, we introduce a two-step approach to Gromov's
h-principle. From formal geometric data, the first step builds a transversely
geometric Haefliger structure of codimension n. This step works on all
manifolds, even closed. The second step, which works only on open manifolds and
for all geometries, regularizes the intermediate Haefliger structure and
produces a genuine geometric structure. Both steps admit relative parametric
versions. The proofs borrow ideas from W. Thurston, like jiggling and
inflation. Actually, we are using a more primitive jiggling due to R. Thom.
