Do bonuses provided by city buildings transfer with your hero to the next scenario mission?

Some cities allow you to construct buildings which provide a buff to any hero that visits that city. Do these bonuses transfer with your hero to later missions, or can I avoid hitting these up if I'm close to completing the mission if they don't transfer?

NB This is actually Heroes Chronicles but I'ven't enough rep to create the new tag.

Example

enter image description here


Yes, the modifier from Wall of Knowledge, Order of Fire, Hall of Valhalla, and Warlord's Cage is permanent.