  A mesoscopic model for heterogeneous DNA denaturation is developed in the
framework of the path integral formalism. The base pair stretchings are treated
as one-dimensional, time dependent paths contributing to the partition
function. The size of the paths ensemble, which measures the degree of
cooperativity of the system, is computed versus temperature consistently with
the model potential physical requirements. It is shown that the ensemble size
strongly varies with the molecule backbone stiffness providing a quantitative
relation between stacking and features of the melting transition. The latter is
an overall smooth crossover which begins from the \emph{adenine-thymine} rich
portions of the fragment. The harmonic stacking coupling shifts, along the
$T$-axis, the occurrence of the multistep denaturation but it does not change
the character of the crossover. The methods to compute the fractions of open
base pairs versus temperature are discussed: by averaging the base pair
displacements over the path ensemble we find that such fractions signal the
multisteps of the transition in good agreement with the indications provided by
the specific heat plots.
