[AngelicaDeAlquezar]

There might be some regional differences, but as I know these expressions:

- Mano a mano: Noun meaning competition or conflict.
· El mano a mano entre los dos académicos no dio ningún ganador. -> Both academics had a discussion and none won.


- Ir de la mano con: To bring along, something happens at the same time as something else.
· El éxito va de la mano con el esfuerzo. -> You can't be successful if you don't make the necessary effort.

- Caminar/ir de la mano de* alguien: To walk hand in hand with someone, to be guided by someone/something.
· El niño va de la mano de su madre.
· La mayor producción va de la mano de las nuevas tecnologías.
* I must say that many people use "ir de la mano con" and "ir de la mano de" as perfect synonyms, meaning both to bring along and to walk hand in hand.