BOSTON (CBS) – Boston students will go back to school Wednesday and the city’s parking ban and snow emergency will be lifted Tuesday evening.

Mayor Thomas Menino made the announcement late Tuesday morning, saying crews have made “significant progress” with snow removal after the weekend blizzard.

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The parking ban and snow emergency will be lifted at 6 p.m. Tuesday and reduced parking rates will expire at 8 p.m.

Menino said drivers should continue to exercise caution, pay attention to “no parking” signs in areas designated for snow removal, and expect delays as crews continue to remove snow.

“Our snow removal teams did great work throughout the night last night,” Menino said.

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“Our crews will be out there all day and again tonight as we continue to widen roads, make our schools safe for students, and respond to residents’ concerns about residential areas.”

Some parents are ready for school to reopen.

“I was very excited,” said West Roxbury mother Tina Ryan. “I was like, Yea!”

Others are concerned about the snowbanks children will have to walk around. “Give the people time to clear out the snow,” said another mom in Dorchester, while she walked with her kids in the street. There were no sidewalks. “It’s too soon in my eyes.”

Crews spent Tuesday clearing sidewalks around the Joyce Kilmer Elementary School in West Roxbury. Mayor Menino says school bus drivers inspected their routes, and school officials planned to visit every facility to make sure they’re safe and ready before they open.

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WBZ-TV’s Christina Hager contributed to this report.