  We construct an infinite family of links which are both almost alternating
and quasi-alternating from a given either almost alternating diagram
representing a quasi-alternating link, or connected and reduced alternating
tangle diagram. To do that we use what we call a dealternator extension which
consists in replacing the dealternator by a rational tangle extending it. We
note that all not alternating and quasi-alternating Montesinos links can be
obtained in that way. We check that all the obtained quasi-alternating links
satisfy Conjecture 3.1 of Qazaqzeh et al. (JKTR 22 (06), 2013), that is the
crossing number of a quasi-alternating link is less than or equal to its
determinant. We also prove that the converse of the Theorem 3.3 of Qazaqzeh et
al. (JKTR 24 (01), 2015) is false.
