The city auditor, as clerk, shall keep an accurate record of all changes made in valuation, and of all other proceedings, and, within ten days after the completion of the equalization of the assessment, shall deliver the assessments as equalized to the county auditor of the county in which the city is situated, with the city auditor’s certificate that the assessments are correct as equalized by the city board of equalization. The assessment as equalized must be accepted by the board of county commissioners in lieu of all other assessment rolls for the property in said city.