  We introduce and study notions of bigraded formality for the algebra of forms
on a complex manifold, along with their relation to higher
Aeppli-Bott-Chern-Massey products which extend the case of triple products
studied by Angella-Tomassini. We show that these Aeppli-Bott-Chern-Massey
products on complex manifolds pull back non-trivially to the blow-up along a
complex submanifold, as long their degree is less than the real codimension of
the submanifold.
