Azimuthal spin asymmetries, both for charged and neutral pion production in semi-inclusive deep inelastic scattering of unpolarized charged lepton beams on longitudinally and transversely polarized nucleon targets, are analyzed and calculated. Various assumptions and approximations in the quark distributions and fragmentation functions often used in these calculations are studied in detail. It is found that different approaches to the distribution and fragmentation functions may lead to quite different predictions on the azimuthal asymmetries measured in the HERMES experiments, thus their effects should be taken into account before using the available data as a measurement of quark transversity distributions. It is also found that the unfavored quark to pion fragmentation functions must be taken into account for $��^-$ production from a proton target, although they can be neglected for $��^+$ and $��^0$ production. Pion production from a proton target is suitable to study the $u$ quark transversity distribution, whereas a combination of pion production from both proton and neutron targets can measure the flavor structure of quark transversity distributions.

31 latex pages, 13 figure, to appear in PRD