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The Eastern Orthodox and Roman Catholics share the same basic list of saints prior to the Great Schism of 1054. Besides having divergent saints since then, the two Communions have a different Ecclesiology when it comes to nominating saints. Roman Catholics have a formal multistep process for a person to be eventually nominated and elevated, while Eastern Orthodox use the older, more informal method of simply relying on the popular acclaim of the people for such considerations. Besides this, I have heard that Roman Calendar has been revised as far as feast days go (older less popular saints removed to make room for more recent and venerated personalities).
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Yes, recognised in the sense that they can never be rejected as a saint.
A saint is someone in heaven.
Therefore St. Isaac of Nineveh is either in heaven or not. The Catholic church is "one", that would mean that St. Isaac of Nineveh cannot be a saint in the Catholic Church in Damascus and cease to be a saint in Paris.
St. Isaac of Nineveh is either in heaven or not, and if one part of the one Church declares an individual in heaven, it would make no sense for a church to call itself "one" and have conflicting irreversible supernatural declarations.