Finally I figured out that I only needed to configure two replications from my local CouchDB.
Here are both replications:
{
"source":"https://username:pwd@username.cloudant.com/cloud_db",
"target":"http://username:pwd@localhost:5985/local_db"
}
{
"source":"http://username:pwd@localhost:5985/local_db",
"target":"https://username:pwd@username.cloudant.com/cloud_db"
}
Now, in http://localhost:5984/_utils/status.html
there are two replications running.
Note that I added the username and password to the local connection too. That's because you need to be an authorized user in order to replicate design documents.
Thanks a lot Mike, your answer helped a lot!