Acquisitions: Do companies pay Equity Value, but total cost/value of transaction is Enterprise Value?

I was wondering if a company, when acquiring another, has to pay only for the Equity Value (in order to become controlling shareholder = buy shares), but the total cost of the transaction is measured by Equity Value + Net Debt, as the acquirer becomes also the new debtor, that is, the debt act as a "cost", although it does not happen as a payment itself.