Motivated by the peculiar features observed through intrinsic tunneling spectroscopy of Bi 2 Sr 2 CaCu 2 O 8+␦ mesas in the normal state, we have extended the normal-state two-barrier model for the c-axis transport ͓M. Giura et al., Phys. Rev. B 68, 134505 ͑2003͔͒ to the analysis of dI / dV curves. We have found that the purely normal-state model reproduces all the following experimental features: ͑a͒ the parabolic V dependence of dI / dV in the high-T region ͑above the conventional pseudogap temperature͒, ͑b͒ the emergence and the nearly voltage-independent position of the "humps" from this parabolic behavior by lowering the temperature, and ͑c͒ the crossing of the absolute dI / dV curves at a characteristic voltage V ϫ . Our findings indicate that conventional tunneling can be at the origin of most of the uncommon features of the c-axis transport in Bi 2 Sr 2 CaCu 2 O 8+␦ . We have compared our calculations to experimental data taken in severely underdoped and slightly underdoped Bi 2 Sr 2 CaCu 2 O 8+␦ small mesas. We have found good agreement between the data and the calculations, without any shift of the calculated dI / dV on the vertical scale. In particular, in the normal state ͑above T ء ͒ simple tunneling reproduces the experimental dI / dV quantitatively. Below T ء quantitative discrepancies are limited to a simple rescaling of the voltage in the theoretical curves by a factor ϳ2. The need for such modifications remains an open question, that might be connected to a change of the charge of a fraction of the carriers across the pseudogap opening.