  Binary clustering systems are closely related to monotone transit functions.
An interesting class are pyramidal transit functions defined by the fact that
their transit sets form an interval hypergraph. We investigate here properties
of transit function $R$, such as union-closure, that are sufficient to ensure
that $R$ is at least weakly pyramidal. Necessary conditions for pyramidal
transit functions are derived from the five forbidden configurations in
Tucker's characterization of interval hypergraphs. The first corresponds to
$\beta$-acyclicity, also known as total balancedness, for which we obtain three
alternative characterizations. For monotonous transit functions, the last
forbidden configuration becomes redundant, leaving us with characterization of
pyramidal transit functions in terms of four additional conditions.
