(a) The assessors shall at once proceed to inscribe in a book to be used for that purpose the description of each of the lots, blocks, or parcels of land, and railroad tracks and rights-of-way and shall assess the value of the benefit to accrue to each of the lots, blocks, or parcels of land, and railroad tracks and rights-of-way by reason of such improvement, which assessment of benefits they shall enter upon the book opposite the description thereof.
(b) They shall then subscribe the assessment and deposit it in the office of the city clerk, where it shall be kept and preserved as a public record.
(c) The assessment may be annually readjusted as provided in this chapter.
(d)
(1) The assessors, or their successors, or a majority of them, may file with the city clerk their certificate correcting erroneous descriptions of the lots, blocks, and rights-of-way, or describing the lots, blocks and rights-of-way where the description was in the original assessment defective or wholly or partly omitted.
(2) Upon the filing of the certificate, the city clerk shall extend or set out in the book the corrected or supplied descriptions, and the descriptions shall relate back to the filing of the assessment in the first instance and shall have the same force and effect as if correctly assessed and described and filed at that time.