上げる => to finish doing ~ N3
[上「あ」]げる => Just finished/completed A N3
Time, Situation
は~で有名 => famous for ~ N3
あげる => ...Up (Upwards) N4
Direction
ふりをする => to pretend; to act as if ~ N3
させてあげる => (Allow) N4
Allow
ふりをする => To pretend to (be) A N3
Adjectival, Description
てあげる => Help, do for N4
Give and take advice
~をかわきりに(~を皮切りに)      => One after another; starting with ~ N1
てさしあげる => Do for N4
Give and take advice
の上で(は)/~上 => according to; from the viewpoint of ~ N2
上 => In terms of... N1
Position, perspective