Is there jealousy among twins?

From what I see day in and day out, I would say yes. There is either jealousy or competiton going on between my twins at least.

Twin B, when not getting her way or what she wants, will slap her sister, Twin A, push her , take away her toy and yet again, bite her.

But lately, I have been catching Twin B before she attempts to hit, push or bite her twin sister. It is so sad to see this happening and it only seems to happen around Mommy (Me) and Daddy.
Once a week, I have a sitter come over and watch my twins for a couple of hours and I ask her if
Twin B ever bites or pushes Twin A and she says no.

So, now I am thinking this is just Twin B's way of getting my attention. The thing is, we do play with each other and I read to her all the time. She loves to be read to, the same book over and over and over and over again.

I am just wondering, is there really jealousy among twins even at the tender ages of 10-17 months old?

I hope not and if so, I will have to break this cycle because this is not right. Even before my twins were born, I was speaking to them and calling them by their names.
I was also talking about them being sisters and how they will love each other and be best friends forever.

The funny thing about them fighting is, they really do love each other. I will be doing whatever in the house, i.e. laundery, dishes, light cleaning and I hear them laughing, giggling and just playing with each other.

Then, all of a sudden, they begin to fight.

It makes me sad to say the least. I will have to begin praying for them to get along...