This article aims to study the behavior of certain types of singularities in a universally equidimensional morphism (i.e., open with constant pure-dimensional fibers). These singularities are those of reduced complex spaces of pure dimension m for which the sheaf LZm (whose sections are meromorphic forms that extend analytically over any desingularization of Z) has depth at least two and are called weakly-1-rational and denoted BR1; for spaces whose singular locus is of codimension at least two, they are called weakly-2-rational and denoted BR2. Our study focuses on the possibility of transferring this type of singularities from the total space to the base, from the base and the fibers to the total space, and from the latter to the fibers.
