Can Phobias & Fears Influence our Children

It's been a question that I have long pondered about...do our children naturally inherit our phobias or are we unknowingly passing our phobias on to our children.

Whilst I'm absolutely terrified of spiders and creepy crawly's . I have always done my best to put a brave face on in front on the kids ..."Oooh it's only a spider it won't hurt you" ("I would say") whilst screaming inside"get me out of here".... So it must have paid off over the years...right...As my eldest son will happily pick up spiders and the other week a hairy caterpillar that found its way in to my slipper...
I let out a mighty scream and my son came to my rescue...my children now being a little older know how I feel about the little critters and just think its me overreacting as usual...but is that because I encouraged them not to be afraid or fear them!!! And I always tell my son's how much more braver they are then me....

At work I have them same issue...working with children we often explore a wealth of bugs and creepy crawly's ..it can be hard to say "Oooh look at the worm"...when all you want do it bolt out the door..although I must admit I once a had a huge spider on my lap whilst a work... I jumped to my feet jumped around like a nutter only to then gather myself as if nothing had happened, replying to the children "Oooh silly me"as they looked on dismayed.
I hate even touching the blinking plastic ones....it's not so bad if they don't look life like
I can handle those ones...but not the big black hard ones...eeeek

Is it important to me that I don't show my fears to my children and those that I work with...so I don't turn them into nervous wrecks...my mum didn't like spiders...and once she threw a yellow pages at one and could remove them if absolutely necessary...Whilst I'm much worse and can't even pick up a dead fly...
What do you think do we pass on our fears and phobias !!!!
I defiantly know that children pick up on our moods and our behaviours and attitudes and feed off of us as adults...so from my experience I can say...we can pass on our fears and phobias to our children.
But what's your experience.....