subsidiary verbs - Just like "ら抜き" is there also "い抜き" such as "見 ている" --> (い抜く) --> "見てる"?

With ichidan verbs, you create potential, and passive voice, as such:

食べられません

If you want to get slangy, you can do "ら抜き" as such:

食べれません

So, is there い抜き as well?

長い間ロンドンに住んでて、いろいろな民族を見ている。

do the "い抜き':

長い間ロンドンに住んでて、いろいろな民族を見てる。

Now:
1. 見てる is actually written in a book.
2. I don't understand how 見てる is a word.
3. In my analysis, 見てる and 見ている have the same meaning.
4. So, just like you can do ら抜き, there is also い抜き?
5. like ら抜き, い抜き is considered slang?

If there is no such thing as い抜き, how is 見てる a word?

Answer

Yes 見てる is a very common contracted form of 見ている. Generally, -ている/-でいる can be contracted into -てる/-でる, and -ています/-でいます can be contracted into -てます/-でます.

見てる as opposed to 見ている may be technically called い抜き, but the word い抜き is far less common than ら抜き. It's because that "い抜き" phenomenon is very common now, and virtually no one thinks い抜き is wrong in not-so-polite conversations. I would say inserting い even sounds weird in casual conversations (for example 今なにしてるの？ is probably more than 100 times more common than 今なにしているの？ in conversations among friends). Native speakers don't have to talk about "い抜き" because they know when and when not to use it even without learning at school.

On the other hand, as of 2016, ら抜き is still considered "non-standard," "slangy," or even "ungrammatical" by some, and there are a lot of debate regarding ら抜き among native speakers.

I don't want to say opinionated things here, but generally, you may eventually need to know how to use "い抜き" properly, but you may not need to use ら抜き at all.