Do they believe in a transition or intermediate state of being before heaven?
By Heaven, are you referring to the spiritual abode of God or the World to Come? Because it appears that you are referring to our eschatological final destination.
I suggest, because this is a complex issue, and the Eastern Orthodox approach is more complex than the Oriental Orthodox approach, that you bear that in mind first, and then read, with regards to the Eastern Orthodox, Orthodox Dogmatic Theology by Protopresbyter Michael Pomazansky, or The Fount of Wisdom by St. John Damascene (who is interestingly also venerated by the Oriental Orthodox, so what he writes might be more generally applicable), and then with regards to one of the mainstream interpretations within Eastern Orthodoxy, take a look at The State of the Soul After Death.
What both the Eastern and Oriental Orthodox reject is the historic Roman Catholic conception of purgatory, as a condition of being the duration of time one spends in which being determined by the extent to which one has committed venial sins and minus the extent to which one has obtained through various penitential acts and sacramentals plenary indulgences (for example, copies of the Challoner Douai-Rheims Bible printed during the 1960s contain a table showing the indulgences one receives for each hour that one reads it, and also one’s’ time in purgatory can be reduced further by the intercessory prayers of others in the world of the living, and their practices in obtaining indulgences on behalf of the dead, and for this reason there exist purgatorial societies, and people who pray for the “poor souls” destined to spend a long time in Purgatory who have no one to pray for them (this is related to All Souls Day, which were it not for the purgatorial element, would be identical in meaning to the Soul Saturdays in the Orthodox Church), and which historically was also the reason why chantries existed. We likewise are not aware of any means by which the Church (which is, in this case, defined as the Orthodox + any churches that that are doctrinally orthodox and will re-enter into communion with us; thus, no one questions the catholicity of ROCOR or the Orthodox Church of North Macedonia, and in the case of the Antiochian Orthodox they correctly do not question the catholicity of the Syriac Orthodox, or vice versa, and like wise between the Alexandrian Greeks and the Copts, since the ecumenical agreements between these churches have the effect of entrusting the pastoral care of the faithful to the other church, for example, if a Copt marries an Alexandrian Greek, or in the case of the Antiochians and Syriac Orthodox, in general, except in North America, since the Antiochian Church of North America is an autonomous church kind of like the sui juris Eastern Catholic Churches in its relationship with Antioch, that was historically a part of the Russian Orthodox Church, until the schisms caused by the Soviet Union which caused the Russian Orthodox Church in North America to be split between what would become the OCA, the AOCNA, and to a lesser extent ROCOR, and to a much lesser extent the Patriarchal parishes) has control over a treasury of merit accumulated by the saints, which it can release in the form of indulgences.
This whole construct of Purgatory as a place of temporal punishment for sins which have been spiritually forgiven, which is ameliorated by penitential acts and offerings in response to which the church grants indulgences from a treasury of merit that has accumulated from the actions of the saints and over which the church has such specific control as to be able to reduce one’s time in purgatory by a specific amount in response to obtaining a specific indulgence granted for a specific action, such as making a pilgrimage or wearing the Brown Scapular or having a mass or the Office of the Dead said in one’s name, is what we reject as purgatory.
I would argue that in many respects the Orthodox view is potentially more intimidating to the poorly catechized than the historic Roman Catholic purgatorial construct with all of its distinctive attributes as described above, which likely appeared in the Scholastic period (since, while some church Fathers spoke of a cleansing of the souls of the saved, we don’t find anything like the elaborate system of the treasury of merit and indulgences for specific actions, or anything which could be read in such a way as to imply the existence of such, in the writings of the Greek or Syrian fathers); it is possible that the Purgatorial system was implemented in the Scholastic period based on the well-known desire of the Schoolmen to refine and clarify with greater precision the definitions of the faith employed by the Roman church. and furthermore to moderate what may have, in the West, seemed like a poorly defined and overly frightening system.
It is certainly the case that the Roman system did have the effect of promoting morality, and the abuse of it for financial purposes through the sale of indulgences was a short lived phenomena, which was completely abolished by the Council of Trent (Ironically, of the 95 theses, most of them revolved around this, so had Pope Leo X simply done this a few decades earlier, he could likely have forestalled the schism between the Roman Catholics and the Lutheran countries of Northern Europe, which would have made the schism between the Roman and English churches less likely. It is not clear that this would have prevented the Calvinist schism, but it would have prevented or delayed the separation of most Western Christians.
If you need any help accessing any of the books I have mentioned, please let me know.