  We consider a family of spherically symmetric, asymptotically Euclidean
manifolds with two trapped sets, one which is unstable and one which is
semi-stable. The phase space structure is that of an inflection transmission
set. We prove a sharp local smoothing estimate for the linear Schr\"odinger
equation with a loss which depends on how flat the manifold is near each of the
trapped sets. The result interpolates between the family of similar estimates
in \cite{ChWu-lsm}. As a consequence of the techniques of proof, we also show a
sharp high energy resolvent estimate with a polynomial loss depending on how
flat the manifold is near each of the trapped sets.
