How did the birth of mary present a bridge between the gothic and the renaissance periods? what was different in this artwork that influenced the artists of the renaissance?

Good question, im not 100% sure but heres my guess,The Florentine School of Painting is characterized by the naturalism in painting in Florence that started to emerge in the 13th century.

The period between 1200 and 1400 in Italy provides an important bridge in Art History between the Medieval period and Byzantine and Gothic styles , and the Early Modern period and Renaissance styles.

Painters began to embrace the more naturalistic styles. Harkening back to classical figures, they created images portraying strong emotion and that paid attention to relationships between figures. Their painting expressed a type of realism not present in Byzantine styles.

Florence

Painters in this city wholeheartedly embraced naturalist styles. Harkening back to classical figures, they created images with attention to portraying strong emotions and relationships between figures—painting that expressed a type of realism not present in Byzantine styles.

One painter who demonstrated the shift that was occurring in Florentine painting during this time is Cimabue (c.1240-1302). In his Maesta the viewer may observe elements of both the earlier Byzantine style of painting, as well as the emerging Renaissance style. The work retains the gold background that was familiar in Byzantine icons , and his figures are rendered in a Byzantine style. However, Cimabue made efforts to create space in this work, which would become an important aspect in Renaissance art. His angels surrounding the Virgin and Child overlap one another to indicate space and Cimabue paid great attention to the Virgin’s throne to create a realistic depiction of space as well.