If you want to login to a Linux instance from other Linux instance without password or without mentioning the key, then ssh equivalency is the solution.
Normally, in order to generate ssh equivalency between 2 Linux instances, you create both public and private keys, then copy them over to other instance and add it to authorized_keys file etc.
But in EC2 instance in AWS, you have to create or specify the keys during the launch time of instance. When you launch an EC2 instance, public keys are already present in home directory of the user. For example, for Amazon Linux , the public key would be already present in /home/ec2-user/.ssh/authorized_keys file. That is why, you only need the private key to ssh into that server.
Let's say you have another EC2 instance which is Linux based and you want to establish ssh equivalency between these two instances. Let's suppose both are using the same key-pair. It means that both would already have public key present in their /home/ec2-user/.ssh/authorized_keys file. In that case all you need to do is following on both servers to establish ssh equivalency:
1- Login to Instance 1
2- Go to /home/ec2-user/.ssh/ directory
3- Touch a new file
chmod 700 id_rsa
4- Copy the content of your pem key and paste it into this id_rsa file
Now you should be able to ssh to the other server, which has the same keypair.
Repeat above steps on other server if you want to enable reverse ssh equivalency.