Wow, thank you so much. It works, my topology is not the triangle one, it consists of just one switch and 3 hosts connected to its ports, but no matter, pings work correctly, there’s connectivity.
I do not know whether this other problem belongs to this forum, if this is not the case, tell me, no worries.
I would like to access to a mysql database service which is listening on all interfaces, I can access to it from my host machine typing the following.
mysql -u USER -h 10.0.3.4 -p
or from another VM specifying the ip which belongs to the same private network of the other VM.
I see. You can also use localhost when you run it in the host machine. It makes sense that it works when using the IP used in the NAT network (or similar type) of interfaces in your VM. Nothing strange so far.
However, when trying to access to it from h3, it is not possible, connection timed out.
I can access to it in this way:
mysql -u USER (-h localhost) -p
Do you know what could it be due to?
The reasons could be multiple 
, I cannot imagine just one particular reason right now. Since you have connectivity, I am not sure what is wrong. To start, you can try to use Wireshark at root-eth0 and see if any packet is missing or something makes no sense (see end of post).
It happens the same with another application I would like to run (EJBCA) I can both access to it from my host machine and from another, but not from mininet.My ufw firewall is disabled.
I thought it has something to do with mininet as when accessing to the service from another VM it works. But doing the same in mininet leads to that problem.
Checking the ufw is a smart thing, it was a good idea. I solve most of my issues with Wireshark when it comes to problems like this. Check next paragraph 
EDIT:
Oh I might have found the error. I’ll give you some steps to find the solution. But I will let you discover it on your own. Try to run a netcat session, a TCP one like this.
Run this on host machine:
nc -l 11111 #sorry wrong port before
Run this on H3:
nc 10.0.3.4 11111
If the connection is successful (i.e., TCP session is OK, but it won’t be the first time you do this command from H3), then whatever you write in H3’s console will appear at host machine’s console. If you open Wireshark listening at root-eth0, it will tell you there is an error with packet’s coming back from host machine to H3. Read the error and the suggestion it gives you about the checksum. Let’s see if you can solve that on your own, else send another message and I will help you further right away.
Cheers,