上がる=rise, go up,climb up, come(go)in, make progress, improve, promoted, be raised, finish, 彼は階段を上がってきた He came up the stairs. はしごで屋根に上がった I climbed up the ladder to the roof. どうぞ，お上がりください Please come in. いつそれをいただきに上がりましょうか When shall I call [come] for it? 弟は来年学校へ上がる My brother enters elementary school next year. 風呂から上がったばかりだ He has just finished bathing. 彼は課長に上がった He was promoted to section chief. 急に体温が上がった His temperature rose suddenly. 柔道の腕が上がった He has gotten better at judo.／His skill in judo has improved. バス料金が160円から190円に上がった The bus fare went up from 160 yen to 190 yen. 費用はとても安く上がった It was far less expensive than (we) expected. 作品はきれいに上がった The work turned out beautifully. 梅雨がやっと上がった At last the rainy season came to an end. 川から水死体が上がった A drowned body was found in the river. 挙がる=be arrested, be nabbed, be mentioned, be cited, to be listed (as a candidate) 彼が有罪だという証拠が挙がった We have found evidence which proves his guilt. 殺人犯人はまだ挙がらない The murderer is still at large. ついに犯人が挙がった The criminal was arrested at last.／The police have finally picked up the criminal. 揚がる=be (deep)fried,land, 夜空に花火が揚がった Fireworks were set off in the night sky. たくさんの凧(たこ)が揚がっている There are many kites flying in the sky. えびがからっと揚がった The shrimps were fried crisp. どっと笑い声が揚がった There was a sudden burst [roar] of laughter. 計画に対して反対の声が揚がった There was an outcry against the plan. 水夫たちが船から揚がってきた The sailors came ashore. 乗客たちは陸に揚がった The passengers landed.

I think 上がる　measn go up,rise...Some stuff go up and move from low area to high area. 挙がる　means sometimes be cited, be mentioned, be arrested and so on. 揚がる　means hoist,be fried...

挙がる and 揚がる are just alternatives, and I never see them used. Maybe in ancient writings or something.

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