“Being sustained, Ānanda, he is sustained by the supreme sustenance; for this—the dimension of neither perception nor non-perception—is the supreme sustenance. There is (however) the case where a monk, having practiced in this way—‘It should not be, it should not occur to me; it will not be, it will not occur to me. What is, what has come to be, that I abandon’—obtains equanimity. He does not relish that equanimity, does not welcome it, does not remain fastened to it. As does not relish that equanimity, does not welcome it, does not remain fastened to it, his consciousness is not dependent on it, is not sustained by it [does not cling to it]. Without clinging/sustenance, Ānanda, a monk is totally unbound.”
“It’s amazing, lord. It’s astounding. For truly, the Blessed One has declared to us the way to cross over the flood by going from one support to the next. But what is the noble liberation?”
“There is the case, Ānanda, where a disciple of the noble ones considers this: ‘Sensuality here & now; sensuality in lives to come; sensual perceptions here & now; sensual perceptions in lives to come; forms here & now; forms in lives to come; form-perceptions here & now; form-perceptions in lives to come; perceptions of the imperturbable; perceptions of the dimension of nothingness; perceptions of the dimension of neither perception nor non-perception: That is an identity, to the extent that there is an identity. This is deathless: the liberation of the mind through lack of clinging/sustenance.’
Could deathless be emptiness? it would make sense then why emptiness isn't included to the way which they mean same thing.
at dimension of neither perception nor non...: that is an identity.., hmm interesting.
https://www.accesstoinsight.org/tipitak ... .than.html
"Now, when the monk is percipient of himself here,
then from there to there, step by step, he touches the peak of perception. As he remains at the peak of perception, the thought occurs to him, 'Thinking is bad for me. Not thinking is better for me. If I were to think and will, this perception of mine would cease, and a grosser perception would appear. What if I were neither to think nor to will?'  So he neither thinks nor wills, and as he is neither thinking nor willing, that perception ceases  and another, grosser perception does not appear. He touches cessation. This, Potthapada, is how there is the alert  step-by step attainment of the ultimate cessation of perception.
at 8 jhana monk is percipient of himself.
“Now, Ānanda, I have taught the practice conducive to the imperturbable. I have taught the practice conducive to the dimension of nothingness. I have taught the practice conducive to the dimension of neither perception nor non-perception. I have taught the way to cross over the flood by going from one support to the next, the noble liberation. Whatever a teacher should do—seeking the welfare of his disciples, out of sympathy for them—that have I done for you. Over there are the roots of trees; over there, empty dwellings.
Practice jhāna, Ānanda. Don’t be heedless. Don’t later fall into remorse. That is our message to you all.”