  In this paper, we introduce the B-discrete spectrum of an unbounded closed
operator and we prove that a closed operator has a purely B-discrete spectrum
if and only if it has a meromorphic resolvent. After that, we study the
stability of the B-discrete spectrum under several type of perturbations and we
establish that two closed invertible linear operators having quasisimilar
totally paranormal inverses have equal spectra and B-discrete spectra.
