This case is so egregious that the US Supreme Court will almost certainly hope that a New York appellate court will toss the verdicts.
The NY appeals court must intervene to act immediately; otherwise the federal court will have to act - or else. Normally the state appeal process can take months; that is inadequate when a leading candidate for president is threatened with being sequestered and prohibited from campaigning.
I think the appellate process is little likely to "toss the verdicts"; that normally occurs with copious paper work and detailed legal cause for dismissal. I doubt the appellate courts will take on that burden with an emergency appeal. The emergency is obvious - the end of the American Constitutional electoral process. To my untrained mind, a 'stay' is most likely so that the Trump presidential campaign can proceed and later time can be spent on documenting unethical and/or unconstitutional legal abuses.
It is one of the most critical crises in modern history, perhaps ever in our history. Democrat attempts to circumvent the normal electoral process in order to end all opposition to their permanent power shows what criminal traitors they consider themselves - and they do not care that they are perceived that way.☠😠