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I believe you mean "cross-appeal," rather than "cross-complaint."
One party's timely notice of appeal may extend the appeal deadline for any other party to the action: “If one party timely files a notice of appeal, any other party may file a notice of appeal within 14 days after the date when the first notice of appeal was filed, or within the time otherwise prescribed by this Rule 4(a), whichever period ends later.” FRAP 4(a)(3).
Thus, e.g., if one party files a notice of appeal on the 30th day (the last possible day of the appeal deadline), all other parties have 14 more days to appeal … even though they otherwise would have confronted a jurisdictional bar to review had there not been a timely first notice of appeal! Conversely, if the first party's appeal is filed in the first week of the 30-day deadline, other parties must file their notice of appeal within the original 30-day period; the 14-day deadline does not come into play because the 30-day period expires last.
I'm not sure if I've answered your question, because I'm unclear on the precise terminology. I assume you filed an opening brief, and the government, instead of filing an answer brief, filed a notice of cross-appeal. If so, then my answer above is correct -- but, it may not entirely apply to your circumstances. Feel free to clarify and I'll try to help you understand the procedure.
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