  We study the class of planar Feynman integrals that can be constructed by
sequentially intersecting traintrack diagrams without forming a closed
traintrack loop. After describing how to derive a $2L$-fold integral
representation of any $L$-loop diagram in this class, we provide evidence that
their leading singularities always give rise to integrals over
$(L{-}1)$-dimensional varieties for generic external momenta, which for certain
graphs we can identify as Calabi-Yau $(L{-}1)$-folds. We then show that these
diagrams possess an interesting nested structure, due to the large number of
second-order differential operators that map them to (products of) lower-loop
integrals of the same type.
