I receive some conversation that after a while are not relevant for me anymore.
I would like to somehow mute them so that they don't arrive as new and unread emails in my inbox anymore.
Is this achievable?
In New Gmail (introduced in July 2018), it's different:
If you enable Gmail shortcuts, you can click "m" to mute a conversation.
When you mute a message: Any replies stay out of your inbox. You can search for the conversation if you want to find it again.
In Gmail, when viewing the conversation, open the "More" menu and choose "Mute".
Muted conversations will only pop back into your inbox ready for your attention if a new message in the conversation is addressed to you and no one else, or if you're added to the "To" or "Cc" line in a new message.