Bookthickness of covering space

A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the quality of a book embedding which is the minimum number of pages in which the graph G can be embedded.

If a graph $ G$ is a covering graph of graph $ B$ , is there any relation between their pagenumber?

I think the covering graph is more complicated than the basis graph. So does $ pn(G)\geq pn(B)$ hold in general?