We present the definition of metric bundles (MBs) in axially symmetric geometriesand give explicit examples for solutions of Einstein equations. These structures have been introduced in Pugliese and Quevedo (2019) to explain some properties of black holes (BHs) and naked singularities (NSs), investigated through the analysis of the limiting frequencies of stationary observers, which are at the base of a Killing horizon definition for these black hole spacetimes. In Pugliese and Quevedo (2019),we introduced the concept of NSKilling throats and bottlenecks associated to, andexplained by, the MBs. In particular, we proved that the horizon frequency canpoint out a connection between BHs and NSs. We detail this definition in generaland review some essential MBs properties as seen in different frames and exactv solutions.