See @feigin1975characteristic.
Definition Given a manifold M, a flag of foliations of codimensions qk≤qk−1≤⋯≤q1 is a sequence of foliations F1,…,Fk such that for i=1,…,k the codimension of Fi is qi and for i≤j the leaves of Fi are contained in those of Fj. ◼