While there are many inventions that helped industrial cities grow even further, here are three...
The spinning jenny. This was an upgrade from the spinning wheel and made it easier and efficient to create cotton items. This made cotton spinning more popular than it already was and made cotton items more readily available.
Steam engines and steamboats. This made transportation easier, to transport both items and people. Items could be transported from wide ranges, then be sold and become more readily available. People could also be transported to different regions easily.
The telephone. This made it easier to communicate from across wide ranges. People could now easily exchange ideas and even trade with each other in an easier manner. As telephones became more and more common and quickly became a household item, industries had to keep making them.