Removing paragraph breaks between linked text frames

I'm setting up a ~40 page book of one flowing text box copied from a Word document with headings and pictures. I'm wondering if there's an easy way to remove extra spaces between linked frames when a new page begins - for instance, on some pages the text starts on the second line rather than the first line of the text frame because of a paragraph break between it and the previous paragraph on the last page.

I'm sure this is an easy answer but I don't have any formal training or the vocabulary to find a solution on my own. Much appreciated!