  The purpose of this paper is to study the bimeromorphic invariants of compact
complex manifolds in terms of Bott-Chern cohomology. We prove a blow-up formula
for Bott-Chern cohomology. As an application, we show that for compact complex
threefolds the non-K\"{a}hlerness degrees, introduced by Angella-Tomassini
[Invent. Math. 192, (2013), 71-81], are bimeromorphic invariants. Consequently,
the $\partial\bar{\partial}$-Lemma on threefolds admits the bimeromorphic
invariance.
