verbs - Infinitive without to: The first thing I do is open my eyes

I have not been able to find an explanation for this use of an infinitive without to:

The first thing I do in the morning is go to the bathroom.

The first thing I do in the morning is open my eyes.

The first thing I do in the morning is turn off the alarm clock.

Infinitives without to are used in the following cases:

-After modal auxiliary verbs (We can managed it)

-After do (I do admit I was wrong)

-After certain verbs like let, make, see... (They made me wait)

-After rather, better and had better (I would rather go alone)

-After and, or, except, but, than, as and like (It is as easy to smile as frown)

-After why (Why pay more at other shops?)

[ http://www.perfectyourenglish.com/grammar/infinitives-without-to.htm ]

I have found no mention of using an infinite without to after the verb to be. Are the examples above a special case? Are they very colloquial? Or are they incorrect?

Answer

In this case actually infinitive with and without "to" is possible (and I was surprised that "to" is possible here, as it sounds quite uncommon to me).

From bbc.co.uk:

There are one or two other structures where to-infinitive and the bare infinitive are both possible. Expressions with do or did, such as what I've done or all I did can follow either pattern.

I hate shopping so what I've done is (to) order a new computer over the Internet.

All I did was (to) suggest that she should lend him no more money. I didn't insist on it.

The examples you gave are not incorrect in any way, and such structures are commonly used.