Specialized connections between adjacent cells in your heart hold them together closely so that blood does not leak out between the cells as the heart dynamically pumps your blood. The pressure of pumping would blow apart adjacent cells, were they not held tightly together by a second specialized connection. Furthermore, coordinated pumping activity of these cells relies on a third specialization between them. Describe how these three types of intercellular connections (shown at the right) work together in the functioning heart.

It is an organ that pumps blood throughout the body via the circulatory system, supplying oxygen and nutrients to the tissues and removing carbon dioxide and other wastes.

Gap junctions and inter-cellular adhesion:

Gap junctions are responsible for electrical coupling and the transfer of small molecules between cells.
Whereas the desmosome like junctions (also known as adherent junctions) provide strong inter-cellular adhesion

The Specialized connections between adjacent cells in the heart are described as below;

Explanation:

The heart is equipped with three distinct types of inter-cellular junction:

"spot" desmosomes:

The adhesion sites formed by the "spot" desmosome anchor the intermediate-filament cytoskeleton of the cell and those formed by the fascia adherents anchor the contractile apparatus.

"Sheet" desmosomes (or fasciae adherent's):

In anatomy Fascia Adherents are ribbon like structures that stabilizes non-epithelial tissue. They are similar in function to the Zonula Adherents or Adherents junction of epithelial cells. It's a broad inter-cellular junction in the transversal sections of an inter-calated disk of cardiac muscle anchoring actin filaments. It helps to transmit contractile forces.

The intercalated disk:

Unique structural formations found between the myocardial cells of the heart. They play vital roles in bonding cardiac muscle cells together and in transmitting signals between cells.