(a)the appeal is, in the case of a tax assessed on the annual value of buildings or lands or both, brought within thirty days next after the date of the authentication of the assessment list under section 69 (exclusive of the time requisite for obtaining a copy of the relevant entries therein), or, as the case may be, within thirty days of the date on which an amendment is finally made under section 71, and, in the case of any other tax, within thirty days next after the date of the receipt of the notice of assessment or of alteration of assessment or, if no notice has been given, within thirty days next after the date of the presentation of the first bill in respect thereof:
