I can’t speak for other particular Eastern Catholic Churches, but in the Ukrainian Greek Catholic Church none of the greater feasts are transferred. For example even if the Annunciation falls during Holy Week or even Pascha, it is still celebrated with an interesting mix of services.
Lesser feasts may be transferred during Great Lent, Holy Week and the time of the Pentecostarion (Pascha to the Sunday after Pentecost inclusive).
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