Co-dominant traits:
These traits will show up if they have the genetics for it. If they have genetics for it from both parents then they will show up. but as something slightly different (the 'Super' form).
Dominant Traits:
These traits will show up if they have the genetics for said trait, from either or both parents. There is no difference between having only 1 gene telling them to have that trait or 2 genes telling them to have that trait.
Recessive Traits:
These traits will show up ONLY if they have 2 genes telling them to have that trait, in other words each parent has to have at least 1 gene in order for the trait to show in any offspring. Any animal with only 1 gene will show no difference in appearance than if it had no gene telling it to have that trait.
Spiders are dominant. Any offspring NOT showing the trait contain no genetic material telling them, OR any offspring they may have to have that trait.
So if you breed a Spider to a Normal then any offspring not showing the Spider trait is simply a normal.