Context. The meteor shower database of the IAU Meteor Data Center (MDC) is used by the whole community of meteor astronomers. Observers submit both new and known meteor shower parameters to the MDC. Two types of problems may arise during the submission process: If a new observation of an already-known meteor shower is submitted as the discovery of a new shower, a duplicate shower will appear in the MDC. If the submission of a new set of parameters for an existing shower is incorrect, a false duplicate of a known meteor shower will appear in the MDC. The MDC database contains such duplicates and false duplicates, so it is desirable to detect them among the streams already in the database and those delivered to the database as new streams. Aims. We aim to develop a method for objective detection of duplicates among meteor showers and to apply it to the MDC. The method will also enable us to verify whether various sets of parameters of the same shower are compatible and thus reveal the false duplicates. Methods. We suggest two methods based on cluster analyses and two similarity functions among geocentric and heliocentric shower parameters collected in the MDC. Results. We obtained a number of results of varying significance. Seven new showers represented by two or more parameter sets were discovered, revealing the duplicates we searched for. We found full agreement between our results and those reported in the MDC database for 30 showers. The multiple sets of parameters defining these showers are correct since they were identified as duplicates. For 20 showers, the same duplicates as given in the MDC were found only by one method. We found 27 showers for which the number of parameter sets found by both methods is close to the corresponding number in the MDC database. However, we found 56 showers listed in the MDC by more than one set of parameters for which no duplicates were found by either of the applied methods. These showers have false duplicates among their sets of parameters. Conclusions. The obtained results confirm the effectiveness of the proposed approach of identifying duplicates. We have shown that in order to detect and verify duplicate meteor showers, it is possible to apply the objective proposal instead of the subjective approach used so far. We consider the identification of 83 problematic cases in the MDC database, among which at least some duplicates were misclassified, to be a particularly important result. The correction of these cases will significantly improve the content of the MDC database.