Reflexivity, symmetry, transitivity, and equivalence are properties of relations in mathematics. Let's examine each property in turn and determine whether "is smaller than" over the set of eggs in a box satisfies them.

Reflexivity:

A relation is reflexive if every element in the set is related to itself. In other words, for all a in A, (a,a) is in the relation.

"Is smaller than" over the set of eggs in a box is not reflexive because an egg cannot be smaller than itself. Therefore, option C is incorrect.

Symmetry:

A relation is symmetric if whenever (a,b) is in the relation, (b,a) is also in the relation.

"Is smaller than" over the set of eggs in a box is not symmetric because if egg A is smaller than egg B, then egg B is not necessarily smaller than egg A. Therefore, option B is incorrect.

Transitivity:

A relation is transitive if whenever (a,b) and (b,c) are in the relation, (a,c) is also in the relation.

"Is smaller than" over the set of eggs in a box is transitive because if egg A is smaller than egg B and egg B is smaller than egg C, then egg A is also smaller than egg C. Therefore, option A is correct.

Equivalence:

A relation is an equivalence relation if it is reflexive, symmetric, and transitive.

Since "is smaller than" over the set of eggs in a box is not reflexive or symmetric, it cannot be an equivalence relation. Therefore, option D is incorrect.

In conclusion, the correct answer is A) Transitive.