The words "This age", "next age" do not occur in the New Testament.
The word aion occurs in Revelation 28 times always doubled "εἰς τοὺς αἰῶνας τῶν αἰώνων" unto the aion of aions.
(4) And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away.
(1) And he shewed me a pure river of water of life, clear as crystal, proceeding out of the throne of God and of the Lamb.
(2) In the midst of the street of it, and on either side of the river, was there the tree of life, which bare twelve manner of fruits, and yielded her fruit every month: and the leaves of the tree were for the healing of the nations.
(3) And there shall be no more curse: but the throne of God and of the Lamb shall be in it; and his servants shall serve him:
(11) He that is unjust, let him be unjust still: and he which is filthy, let him be filthy still: and he that is righteous, let him be righteous still: and he that is holy, let him be holy still.
(15) For without [outside the new Jerusalem] are dogs, and sorcerers, and whoremongers, and murderers, and idolaters, and whosoever loveth and maketh a lie.
Five more vss. the end.