TITLE: Is the Bott-Chern/Aeppli cohomology determined by the de Rham and Dolbeault cohomologies?
QUESTION [7 upvotes]: Is there an example of two different complex manifolds that have the same de Rham cohomology and Dolbeault cohomology but different Bott-Chern/Aeppli cohomology?

REPLY [9 votes]: As for compact complex surfaces, the Bott-Chern/Aeppli cohomologies are determined by de Rham/Dolbeault cohomologies:this is contained in Lemma 2.3 in:
Teleman, A.: The pseudo-effective cone of a non-Kählerian surface and applications. Math. Ann. 335(4), 965–989 (2006), arXiv:0704.2948.