I receive a pension from the state of Italy based on my work there.
Italy and the USA have an accord, the paperwork toward Italy was handled by SSA.

Is the Italian Pension taxed as regular income? Are there caps or exemptions?

then, no; in general Income received from foreign pensions may be fully or partly taxable to irs, even if you do not receive a Form 1099 or other similar document reporting the amount of the income.however, there are some exemptions based on US tax treaties with particular countries.as you live in the US and receive a pensionpaid by a payor from italy, you must claim your desired treaty withholding exemption on the form, and in the manner specified by the foreign government. If italy, and/or the foreign withholding agent, refuses to honor the treaty claim, you need to make the treaty claim on your income tax return, or other prescribed form, filed with the foreign country. Additionally, you may be able to claim a Foreign Tax Credit on your U.S. federal individual income tax return for any foreign income tax withheld from your foreign pension .