Intersecting Legendrians and blowups

The purpose of this note is to describe the relationship between two classes of Legendre distributions. These two classes are distributions associated to an intersecting pair of Legendre submanifolds, introduced by one of us by analogy with intersecting Lagrangian distributions of Melrose and Uhlmann, and Legendre distributions associated to a fibred scattering structure introduced by the authors. We prove a general result, and also give an example in two dimensions, which shows explicitly the relation between the two spaces in a simple setting.