The filing of the writ of certiorari shall not stay the enforcement of the agency decision; but the agency may do so, or the court of appeals may order a stay upon such terms as it deems proper. When review of or an appeal from a final decision is commenced under sections 14.63 to 14.68 in the court of appeals, any other later appeal under sections 14.63 to 14.68 from the final decision involving the same subject matter shall be stayed until final decision of the first appeal.