Don’t have all the answers you need, but have a bit of research on perhaps something useful for your Equivalence idea. Universes do not exist by themselves, they are mapped to each other, the mapping is what makes them to show existence per human cognition and spiritualities, the universes by themselves are not cognizable:
Know that the Alam-Saghir (Minor Universe) is a copy and a Nemūdār (Vectorial Abstraction) of the Alam-Kabir (Eminent Universe) and whatever is in the Alam-Kabir is also found in Alam-Saghir. So whatever is found within the Alam-Kabir (Eminent Universe) it ought to have a Nemudar (Vectorial Abstraction) within the Alam-Saghir (Minor Universe), otherwise any description of that object is inaccurate and false.
Definition: According to the treatise 10 of Nasafi Chapter 5 Nemudar of the beautitude of the Paradise are the temporal pleasures on this earth and the Nemudar of the torments of the Hell are the sufferings of humanity on this earth. Based upon this description the best translation for the Farsi word Nemudar is ‘Abstraction’ of something in some universe which is projected or imaged into another. Due to this aspect of the projection or imaging then the attribute ‘Vectorial’ is added, so Nemudar is Vectorial Abstraction.
“O Darwish! The relatedness of these universes are brimful with Ishq (Unary Unrestrained Love), every relatedness (say A in one universe is related to B in another universe) serves as mirror (reflects an image of A into B) while the antecedent and precedent (A and B) are actually in love with each other, and both in love with the mirror as well.
Suyuti Al-Ghazali on Muqabala , probably what you need to study:
Mapping one universe to another
“I say (it is my opinion): Since the universe of Shahada (Observables) became an ‘elevator’ towards the universe of Malakut (Spiritual Realms) and Suluk (Voyage) of Sirat-Al-Mustaqim (The Straight Path) refers to this upward glide i.e. the Din (Religion, way of spiritual life) and the resting-places of the Divine Guidance, therefore if there was no relationships and connections between these universes how could then be any form or glide from one to the other?
Due to the Divine Mercy there is‘equivalence’ between the realm of Shahad (Observables) and Malakut (Realm of Spirits) i.e. entities in one realm are corresponded to the entities in the other realm! Perhaps an entity in the Malakut (Realm of Spirits) has multitudes of corresponding entities in this world. Therefore a metaphor (e.g. entering and exiting the light) becomes an ‘exhibited display’ of an analog (of something in the other universe) and therefore corresponds to an entity in another universe and this correspondence is called Al-Mutabaqah.