Who changes identity in OpenID?

Question

OAuth

Colleagues,
when using OpenID to authenticate users for a long period of time, an interesting situation arises - providers periodically change the user's identity and when you log in again, you cannot compare it with the old account.
For example, earlier mail.ru issued
identity = http://my.mail.ru/mail/user/
and now
identity = https://my.mail.ru/mail/user/
Google:

identity = https://www.google.com/accounts/o8/id?id=xxxsecret

and now

identity = https://plus.google.com/1134263392342342341234

Yandex does not lag behind Google:
identity = http://openid.yandex.ru/user/
and now
identity = https://login.yandex.ru/1232414
Here's how to identify a user on autopilot now? It is impossible for the E-mail field, as it can be faked.
Old or not old protocol, maybe cooler and oAuth, but what to do with current authorizations?
While I was compiling this investigation, I already thought to parse the identity in the hostname and compare it by it? Will Yandex move later to https://login.yandex/?