The phrase "built up through" is correct and usable in written English.
It can be used to describe a process of development or accumulation over time.
Example: "Her confidence was built up through years of practice and dedication."
Alternatives: "developed through" or "accumulated through".
He said the cost of the new site could be met by surpluses built up through the business.
It would have involved exploiting a brand built up through years of low-reward service and patient trust for quick financial gain.
Mr. Glasper's way has to do with both looseness and intricacy: a loose frame and intricate, slip-and-slide languages of harmony and especially rhythm, built up through years of experimenting with a steady crew.
Because of the familiarity built up through previous messages, and the effects of the alcohol, when she suggested that she would remove some of her clothes if he did the same, he agreed.
They then hugged, showing the engagement and relationship built up through the collaborative digital video-making process.
MRC supervisors have expressed concern that factors such as the impact of debts built up through student loans are kicking in and luring scientists away from further study.
Rio Tinto's rivals are unlikely to restructure quite as dramatically: Rio has a $39.0 billion debt mountain to contend with, built up through the acquisition of Canada's Alcan in July 2007.
His knowledge of the area's language and customs, his close acquaintance with tribal leaders and their vices, which he handled with no-nonsense incorruptible patience, built up through years of scholarship and experience on the ground, made all the difference.
Perhaps Amazon's greatest strength is its knowledge of customers built up through their buying history, which makes the company a very efficient marketer.
It started gradually, with the Rosie Riveter factory workers helping the war effort, built up through the '60s and '70s (when one-third of all women worked) and continues today.
Sightsavers and the district health authorities used the working relationship built up through ivermectin distribution to address eye disease generally.
