See also the official documentation:
Help Center > Understanding Groups.io accounts > Merging accounts

If you have two or more accounts, you lose the advantage of seeing all messages from your groups in one list using Your Groups and managing muted or followed topics and hashtags.

You can merge the accounts.

(Do it one email address at a time!)

Below are the steps necessary to perform an account merge.

1) Log into the account that you want to deactivate. If you don't know how to log in, instructions can be found here.

2) Pull down the menu at top right and select Account (or browse to https://groups.io/account)

3) In the "Email" field at the top of the page, enter the address you want to merge into (i.e.: overwriting what is already there).

4) Click the "Change Email" button.

5) Groups.io will notify you of the fact that the account already exists, and ask if you want to merge them. 

6) Click the blue button below this notification to confirm your intent to merge.

7) An email will be sent to the destination email address. 

8) Clicking on the link in that email will again take you to the login page.

9) Log in under the destination email address, using either the account password or the "email me a link" button.

10) Click on the blue button to complete the merge. 

If for any reason you can't log into either of the two accounts, the merge is not possible.

If you try to sign in to a group with an email different than that registered, without logging out first, you will get a pop up that offers to merge all the groups under the email entered.

You will get a message: "An email has been sent to with a link that, when clicked, will cause the accounts to be merged and this account to be deleted."

The email with the link will be sent to the destination address (the one you manually entered while still logged in under the other one). So be sure you check the correct email address.

Please take careful note which address you are merging away from ("originating address") and which one you are merging into ("destination address"). If the originating address owns a group, merging away from it is a good way to lose that ownership. Be very sure you know what you're doing before you go down this road.