Nothing that is substantial can be permanent. Only absences (including cessations) are permanent. This is Buddhism 101.
In the Mahayana, Nirvana is the cessation (a permanent absence, never to arise again) of suffering and the causes of suffering.
What does not cease (in the Mahayana) is the continuum of consciousness, which has flowed from beginningless time, and will continue to do so after nirvana; It is a continuum uncontaminated by suffering and it's causes.
The continuum itself is not permanent in that it changes momentarily, just as it does while in Samsara.
Within the scope of the Asanga Mahayana, and the Dzogchen, Mahamudra, and Zen/Chan traditions especially, the continuum of mind is what persists - the base nature of awareness. When we; through choosing to use the mind as both the subject and object of our meditation; become aware of the conceptual narratives that determine our identities, and then strip them away, we are left with just the mirror-like awareness of the mental continuum. It is then that the opportunities of recognising that the narratives of time and being are mere constructs arise. Within the scope of Nagarjuna's Mahayana (the Madhyamaka) we also use anti-philosophy to guide us to an understanding of the essence-lessness of all phenomena, which we believe to be the definitive meaning of Anatta. Himalayan traditions use both Asanga and Nagarjuna together to provide both a conceptual and an experiential approach to achieving the path of insight.