Let's analyze and match the items in List-I with the corresponding logical equivalence in List-II by understanding the principles of logic behind each equivalence.

Statement A: \([(p \cdot q) \supset r] \stackrel{T}{\equiv}[p \supset(q \supset r)]\)

This is a logical equivalence that represents the principle of Exportation. In logical terms, Exportation allows us to transform a conjunction in the antecedent of a conditional statement into a nested conditional statement. Thus, this matches with III. So, A-III is correct.

Statement B: \([p \cdot(q \vee r)] \stackrel{T}{\equiv}[(p \cdot q) \vee(p \cdot r)]\)

This is referred to as the Distribution law, where conjunction (AND) is distributed over disjunction (OR). Thus, this corresponds to I. Hence, B-I is correct.

Statement C: \((p \supset q) \stackrel{T}{\equiv}(\sim q \supset \sim p)\)

This expresses the rule of Transposition, which implies that a conditional is logically equivalent to its contrapositive. Therefore, it correlates with IV. Therefore, C-IV is correct.

Statement D: \([p \vee(q \vee r)] \stackrel{T}{\equiv}[(p \vee q) \vee r]\)

This follows the principle of Association, which indicates that the way in which propositions are grouped in conjunctions or disjunctions does not affect their truth value. Thus, it matches with II. Hence, D-II is correct.

Based on the above analysis, the correct answer is:

A-III, B-I, C-IV, D-II