  We present a novel way to classify Calabi-Yau threefolds by systematically
studying their infinite volume limits. Each such limit is at infinite distance
in Kahler moduli space and can be classified by an associated limiting mixed
Hodge structure. We then argue that the such structures are labeled by a finite
number of degeneration types that combine into a characteristic degeneration
pattern associated to the underlying Calabi-Yau threefold. These patterns
provide a new invariant way to present crucial information encoded in the
intersection numbers of Calabi-Yau threefolds. For each pattern, we also
introduce a Hasse diagram with vertices representing each, possibly
multi-parameter, decompactification limit and explain how to read off
properties of the Calabi-Yau manifold from this graphical representation. In
particular, we show how it can be used to count elliptic, K3, and nested
fibrations and determine relations of elliptic fibrations under birational
equivalence. We exemplify this for hypersurfaces in toric ambient spaces as
well as for complete intersections in products of projective spaces.
