Btw, I don't know if the Vatican has issued canons on the order of all its "sui juris" churches. The order of the diptychs among the Orthodox differ from one Church to another after Russia/Moscow.
Diptychs?
The affirmation of communion.
At every DL, the priest commemorates his bishop (and some the primate/metropolitan)
The bishop, at his DL, commemorates his Holy Synod and its primate.
The primate, at his DL, commemorates the Holy Synod and the Patriarch (or Pope/Catholicos/Archbishop/Metropolitan as it might be).
The autocephalous Patriarch/Pope/Catholicos/Archbishop/Metropolitan commemorates the primates of the other autocephalous Church.
To strike someone from the diptychs, as happened to the Pope of Old Rome after 1017, signals that they-and all those who commemorate their communion with them-are outside the Orthodox communion of the Catholic Church.
When the Patriarch of Moscow dropped the EP from the diptychs a few years ago (for uncanonical interference in the Patriarchate of Moscow), for that brief period the Patriarchate of Moscow and the Ecumenical Patriarchate were not in communion. Which meant that facilities in Great Britain, for instance, that were shared had to cease functions in common during that time.
That is also why it was a big deal that Pope Theodoros II (the Greek/EO Patriarch of Alexandria) was commemorated at the enthronement of Pope Theodoros II (the Coptic/OO Patriarch of Alexandria).
