〜上げる・〜上がる details

write + carry the work through until the thing is finished

kaki ageru

carry the work through until the thing is finished; be finished

徹夜てつやして、なんとか原稿げんこうを書かき上あげた。

tetsuya shite, nantoka genkou o kakiageta.

I pulled an all-nighter and somehow got the manuscript finished. neutral

パン、そろそろ焼やき上あがるころかな。

pan, sorosoro yakiagaru koro kana.

The bread should be about ready to come out. casual

Examples

〜上げる — carry it through: the agent takes the work all the way to a finished result, often with a note of pride or effort

徹夜てつやして、なんとか原稿げんこうを書かき上あげた。

tetsuya shite, nantoka genkou o kakiageta.

I pulled an all-nighter and somehow got the manuscript finished. neutral

三年さんねんかけて、やっと自分じぶんの店みせを作つくり上あげたんだ。

sannen kakete, yatto jibun no mise o tsukuriageta n da.

It took three years, but I finally built a shop of my own. casual

記者きしゃは関係者かんけいしゃの経歴けいれきをすべて調しらべ上あげた。

kisha wa kankeisha no keireki o subete shirabeageta.

The reporter dug up the full background of everyone involved. neutral

職人しょくにんが一ひとつ一ひとつ丁寧ていねいに磨みがき上あげております。

shokunin ga hitotsu hitotsu teinei ni migakiagete orimasu.

Our craftsmen finish every single one of them with care. formal

〜上がる — come out finished: the same completion reported from the thing's own side, with が rather than を

パン、そろそろ焼やき上あがるころかな。

pan, sorosoro yakiagaru koro kana.

The bread should be about ready to come out. casual

三さんか月げつかかったけど、マフラーやっと編あみ上あがったよ。

sankagetsu kakatta kedo, mafuraa yatto amiagatta yo.

It took three months, but the scarf is finally finished. casual

ご飯はんが炊たき上あがったら、十分じゅっぷんほど蒸むらしてください。

gohan ga takiagattara, juppun hodo murashite kudasai.

Once the rice has finished cooking, let it steam for about ten minutes. neutral

終わる
終おわる states only that the activity stopped at its endpoint; 上あげる claims the job was carried all the way through — a finished article exists (書かき上あげる) or nothing is left to do (調しらべ上あげる) — so it refuses a verb that merely occupies time (×遊あそび上あげる).
〜切る
切きる measures completion against the OBJECT and claims nothing was left over (読よみ切きる — every page); 上あげる measures it against the PRODUCT and claims it is now in finished condition, so 磨みがき上あげる praises the polish rather than counting what got polished.

あげる・くれる・もらう
The same verb in two frames — 書かいてあげる puts the writing at someone else's service, 書かき上あげる finishes it; the て-form marks the favor and the ます-stem the completion, and nothing else tells them apart.