New York Consolidated Laws, Civil Practice Law and Rules - CVP § 5520. Omissions;  appeal by improper method

(a) Omissions.  If an appellant either serves or files a timely notice of appeal or notice of motion for permission to appeal, but neglects through mistake or excusable neglect to do another required act within the time limited, the court from or to which the appeal is taken or the court of original instance may grant an extension of time for curing the omission.

(b) Appeal by permission instead of as of right.  An appeal taken by permission shall not be dismissed upon the ground that the appeal would lie as of right and was not taken within the time limited for an appeal as of right, provided the motion for permission was made within the time limited for taking the appeal.

(c) Defects in form.  Where a notice of appeal is premature or contains an inaccurate description of the judgment or order appealed from, the appellate court, in its discretion, when the interests of justice so demand, may treat such a notice as valid.