Angel Heart

Angel Heart (2001-2017 | Action, Drama, Comedy), by Hojo Tsukasa

Doesn't have an official English translation, only unofficially. And 374 of 443 where translated, and are being released weekly

It's about an assassin (trained since a child by a taiwanese mafia), that got só tormented by killing, that it tried to suicide herself by jumping off a building. And her heart got pierced.

But the mafia didn't want to lose one of its most valuable assets, so they stole a donors heart that was already in transport, and made the transplant. So she started having dreams, but it wasn't her dreams, it was the memories of the donor's heart, feeling for the first time, warmth and happiness. But still wanting to be dead, the entity, the soul of the donor's heart, is trying to make her live, cherish for her. So after 1 year, she wakes up.

And so, after escaping the organization, the heart guides to Shinjuku, looking for City Hunter (that is a sweeper, and the husband of the donor's heart)

After some stuff that are somewhat spoiler, City Hunter and the Soul of the heart starts to help her become more of a normal person, losing her assassin's habits, helping others, enjoying life in its fullest. It has a lot of arcs that are emotional trainracks, I rarely cry for some type of media. At least it isn't only a trainrack of sadness, but also of happiness, warmth, ect

And this thing isn't only with the main characters, happens with the secondary characters and even temporary characters that only appear in one single arc. There is great character development

The manga has a timespan of about 6-7 years

And an extra

It's a City Hunter spin off (1985 Shounen manga, made by Hojo too), an alternate universe. But the only thing they share is most of the main cast and their personalities. But the story and backstory from them are totally different. So no obligatory need to read City Hunter (but i still recommend it)

And if you already liked City Hunter, remember, City Hunter is City Hunter, Angel Heart is Angel Heart

Angel Heart isn't City Hunter (but has a lot of elements of it)