  We analyse line bundle cohomologies on all favourable co-dimension two
Complete Intersection Calabi Yau (CICY) manifolds of Picard number two. Our
results provide further evidence that the cohomology dimensions of such line
bundles are given by analytic expressions, which change between regions in the
line bundle charge space. This agrees with recent observations of CY line
bundles presented in Refs [1,2]. In many cases, the expressions for bundle
cohomology dimensions are polynomial functions of the line bundle charges (of
degree at most 3), and the regions are cones. A more novel observation is that
for some CICY manifolds, the cohomologies are more succinctly determined by
recursive relationships. There can also be boundaries between regions where a
polynomial fit fails, and we link these exceptional cases to irregular
behaviour of the index of the line bundle. Finally, our observations provide
evidence for similarities in the line bundle cohomologies for CICY manifolds
that share rows in the configuration matrix. Among such related CICY manifolds,
we find both that the line bundle charge space is partitioned in the same
manner, and that the same, or closely related, analytical descriptions apply
for the cohomology dimensions in these regions.
